please let me know if you can do it within 7 hours for what price?

Anonymous
timer Asked: Aug 1st, 2015

Question Description

I am sending you two reports, one named sample which is to be used as reference and the one one named project 2 which is the one to be answered. I need to answer Tabs 7.3, 7.4, 7.5, and chapter 7 summary 


Group Project II Sample.xlsx 

Section 1 Group 1 - Project 2.xlsx

PROJECT 1 - PERFORMANCE LAWN EQUIPMENT Washington State University Management 514 - Business Analytics Section 1, Group 1 Laura Assem Vincent Murphy Raul Gonzalez Chapter 6 Summary 6.1: 6.2: 6.3: 6.4: 6.5: Blade Weight The sample distribution to the mean is approximately normal (sample size >= 30 per the CLT) The mean is approx: 4,99 The std deviation is: 0,10928756 The std error is: 0,005841666 6.5: Blade Weight Please see tab 'Ch6.6 - Blade Weight' for details Sampling Error Sample Size 0,2 2 0,1 5 The existing sample set of 350 was used an estimate for the population standard deviation, which enabled us calculate t size. To find a mean blade weight with a sampling error of at most 0.2 with 95% confidence, a new sample size of 2 blad be measured. To find a mean blade weight with a sampling error of at most 0.1 with 95% confidence, the sample size m to 5 (as amount of error required decreases, the sample size must increase). ch enabled us calculate the new sample ew sample size of 2 blade weights must ence, the sample size must be increased Blade Weight Sample Weight 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 4,88 4,92 5,02 4,97 5,00 4,99 4,86 5,07 5,04 4,87 4,77 5,14 5,04 5,00 4,88 4,91 5,09 4,97 4,98 5,07 5,03 5,12 5,08 4,86 5,11 4,92 5,18 4,93 5,12 5,08 4,75 4,99 5,00 4,91 5,18 4,95 4,63 4,89 5,11 5,05 5,03 5,02 4,96 Sorted weight 4,63 4,73 4,74 4,75 4,76 4,77 4,78 4,79 4,81 4,81 4,81 4,81 4,81 4,81 4,81 4,82 4,82 4,82 4,84 4,85 4,85 4,85 4,85 4,85 4,86 4,86 4,86 4,86 4,86 4,86 4,87 4,87 4,87 4,87 4,87 4,87 4,87 4,87 4,87 4,88 4,88 4,88 4,88 Weight Mean 4,9908 Standard Error 0,00584167 Median 4,99 Mode 5,02 Standard Deviation0,10928756 Sample Variance 0,01194377 Kurtosis 11,3784693 Skewness 1,42374184 Range 1,24 Minimum 4,63 Maximum 5,87 Sum 1746,78 Count 350 Min Max Mean Sample Size Range # of Buckets Bucket Width 4,63 5,87 4,9908 350 1,24 9 0,13777778 Bucket # Bucket 1 Bucket 2 Bucket 3 Bucket 4 Bucket 5 Bucket 6 Bucket 7 Bucket 8 Bucket 9 Bucket 10 Bucket 4,63 4,77 4,91 5,04 5,18 5,32 5,46 5,59 5,73 5,87 Frequency Results do not show a perfect normal distribution, hoever they are close. 1 4 65 184 87 7 1 0 0 1 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 5,04 4,93 5,06 5,07 5,00 5,03 5,00 4,95 4,99 5,02 4,90 5,10 5,01 4,84 5,01 4,88 4,97 4,97 5,06 5,06 5,04 4,87 5,00 5,03 5,02 5,02 5,06 5,21 5,09 4,97 5,01 4,90 4,89 4,93 5,16 5,02 5,01 5,10 5,03 5,07 4,92 5,08 4,96 4,74 4,91 5,12 5,00 4,88 4,88 4,88 4,88 4,88 4,88 4,88 4,88 4,88 4,89 4,89 4,89 4,89 4,89 4,89 4,89 4,89 4,89 4,89 4,89 4,89 4,9 4,9 4,9 4,9 4,9 4,9 4,91 4,91 4,91 4,91 4,91 4,91 4,91 4,91 4,91 4,91 4,91 4,91 4,91 4,92 4,92 4,92 4,92 4,92 4,92 4,92 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 4,93 4,88 4,88 4,81 5,16 5,03 4,87 5,09 4,94 5,08 4,97 5,23 5,12 5,09 5,12 4,93 4,79 5,10 5,12 4,86 5,00 4,94 4,95 4,95 4,87 5,09 4,94 5,01 5,04 5,05 5,05 4,97 4,96 4,96 4,99 5,04 4,91 5,19 5,03 4,99 5,12 4,97 4,88 5,07 5,01 4,89 4,95 4,92 4,92 4,92 4,92 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,93 4,94 4,94 4,94 4,94 4,94 4,94 4,94 4,94 4,94 4,94 4,94 4,94 4,95 4,95 4,95 4,95 4,95 4,95 4,95 4,95 4,95 4,95 4,95 4,95 4,95 4,96 4,96 4,96 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 5,09 5,09 4,89 4,93 4,85 5,03 4,92 5,09 4,99 4,92 4,87 4,90 5,02 5,21 5,02 4,9 5 5,16 5,03 4,96 5,04 4,98 5,07 5,02 5,08 4,85 4,9 4,97 5,09 4,89 4,87 5,01 4,97 5,87 5,33 5,11 5,07 4,93 4,99 5,04 5,14 5,09 5,06 4,85 4,93 5,04 5,09 4,96 4,96 4,96 4,96 4,96 4,96 4,96 4,96 4,96 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,97 4,98 4,98 4,98 4,98 4,98 4,98 4,98 4,98 4,99 4,99 4,99 4,99 4,99 4,99 4,99 4,99 4,99 4,99 4,99 4,99 5 5 5 5 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 5,07 4,99 5,01 4,88 4,93 5,1 4,94 4,88 4,89 4,89 4,85 4,82 5,02 4,9 4,73 5,04 5,07 4,81 5,04 5,03 5,01 5,14 5,12 4,89 4,91 4,97 4,98 5,01 5,01 5,09 4,93 5,04 5,11 5,07 4,95 4,86 5,13 4,95 5,22 4,81 4,91 4,95 4,94 4,81 5,11 4,81 4,97 5 5 5 5 5 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,01 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,02 5,03 5,03 5,03 5,03 5,03 5,03 5,03 5,03 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 5,07 5,03 4,81 4,95 4,89 5,08 4,93 4,99 4,94 5,13 5,02 5,07 4,82 5,03 4,85 4,89 4,82 5,18 5,02 5,05 4,88 5,08 4,98 5,02 4,99 5,02 5,03 5,02 5,07 4,95 4,95 4,94 5,12 5,08 4,91 4,96 4,96 4,94 5,19 4,91 5,01 4,93 5,05 4,96 4,92 4,95 5,08 5,03 5,03 5,03 5,03 5,03 5,03 5,03 5,03 5,03 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,04 5,05 5,05 5,05 5,05 5,05 5,05 5,06 5,06 5,06 5,06 5,06 5,06 5,06 5,07 5,07 5,07 5,07 5,07 5,07 5,07 5,07 5,07 5,07 5,07 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 4,97 5,04 4,94 4,98 5,03 5,05 4,91 5,09 5,21 4,87 5,02 4,81 4,96 5,06 4,86 4,96 4,99 4,94 5,06 4,95 5,02 5,01 5,04 5,01 5,02 5,03 5,18 5,08 5,14 4,92 4,97 4,92 5,14 4,92 5,03 4,98 4,76 4,94 4,92 4,91 4,96 5,02 5,13 5,13 4,92 4,98 4,89 5,07 5,07 5,08 5,08 5,08 5,08 5,08 5,08 5,08 5,08 5,08 5,08 5,08 5,09 5,09 5,09 5,09 5,09 5,09 5,09 5,09 5,09 5,09 5,09 5,09 5,09 5,1 5,1 5,1 5,1 5,11 5,11 5,11 5,11 5,11 5,11 5,11 5,12 5,12 5,12 5,12 5,12 5,12 5,12 5,12 5,12 5,13 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 4,88 5,11 5,11 5,08 5,03 4,94 4,88 4,91 4,86 4,89 4,91 4,87 4,93 5,14 4,87 4,98 4,88 4,88 5,01 4,93 4,93 4,99 4,91 4,96 4,78 5,13 5,13 5,13 5,14 5,14 5,14 5,14 5,14 5,14 5,16 5,16 5,16 5,18 5,18 5,18 5,18 5,19 5,19 5,21 5,21 5,21 5,22 5,23 5,33 5,87 Mean Std Dev Std Error 4,9908 0,109288 0,005842 - We can assume a normal distribution since the sample size is >= 30 (per the Central Limit Theorum (CLT)) 18,70829 <-- higher than needed Frequency 200 180 160 140 120 100 Frequency 80 60 40 20 0 4,63 4,77 4,91 5,04 5,18 5,32 5,46 5,59 5,73 5,87 4,63 4,77 4,91 5,04 5,18 5,32 5,46 5,59 5,73 5,87 Frequency Just use the Use a two tailed test Mean Standard Deviation Confidence Level Alpha z Sampling Error Sampling Size 4,9908 (from Blade Weight Data Set - see tab 'Ch6.5 - Blade Weight') 0,109288 (from Blade Weight Data Set - see tab 'Ch6.5 - Blade Weight') 95% 5% 1,96 Critical value 0,2 2 0,1 5 - Blade Weight') - Blade Weight') 2014 Customer Survey Region NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA Quality Ease of UsePrice 4 4 4 5 5 5 5 5 4 4 4 5 5 4 5 5 5 5 4 4 4 4 5 5 5 5 5 4 5 5 5 4 4 5 5 5 5 5 4 5 5 5 5 1 4 5 4 4 5 4 5 4 5 5 5 4 5 4 5 4 4 5 4 4 3 5 3 4 5 5 4 4 1 4 5 4 3 5 4 5 5 3 4 4 5 4 Service 3 4 4 4 5 3 4 4 4 4 1 4 3 4 3 2 2 2 4 5 2 3 2 4 4 2 5 5 4 5 3 1 3 4 2 4 4 4 3 4 3 1 5 Record # 4 5 3 4 4 5 2 5 5 5 4 4 3 4 5 5 5 5 4 4 4 4 5 3 5 5 3 4 4 5 5 4 5 4 4 4 4 5 5 3 4 5 4 1 2 Row Labels China Eur NA Pac SA Grand Total China Eur NA Pac SA China Eur NA Pac SA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 5 5 5 5 5 5 5 5 5 5 4 5 5 5 4 5 4 5 5 5 5 4 4 5 5 5 5 5 5 5 5 5 4 3 5 4 3 1 4 5 4 5 5 4 5 5 4 4 5 5 4 4 4 4 4 5 4 3 4 5 5 4 4 5 5 5 4 4 4 4 4 4 4 5 4 4 3 4 4 5 5 5 4 2 4 5 5 5 5 5 2 4 4 3 2 4 3 4 4 4 1 5 3 4 5 4 5 4 4 5 5 5 3 4 5 5 4 4 3 5 4 4 5 4 5 1 3 2 4 3 4 3 3 4 5 4 4 4 5 5 4 4 5 4 4 4 5 4 5 4 5 5 4 5 5 4 5 4 4 5 4 2 5 5 4 5 4 5 4 2 5 5 5 5 5 4 5 5 4 5 4 5 5 4 5 4 4 NA NA NA NA NA NA NA NA NA NA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA 5 5 4 5 4 5 4 5 4 4 5 5 5 4 5 4 5 4 4 4 5 3 5 5 4 4 1 5 4 4 5 4 4 3 5 4 4 4 4 4 5 4 5 5 4 4 5 5 5 5 5 4 5 5 5 5 5 4 4 4 2 4 5 4 5 4 4 4 3 4 4 4 4 5 4 4 4 4 4 4 3 4 4 5 1 5 4 4 4 5 5 4 4 4 4 5 5 4 5 3 2 5 4 5 3 2 5 4 4 2 4 3 4 2 3 5 3 2 3 3 3 2 4 5 2 5 4 4 4 4 5 4 4 4 3 4 4 4 2 4 4 3 5 3 5 5 4 4 4 3 4 5 4 5 5 5 5 4 5 3 4 4 5 4 5 4 5 4 4 4 5 4 5 3 5 4 1 5 5 4 5 4 5 3 4 4 5 5 SA SA SA SA SA SA SA SA SA SA SA SA SA Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Pac Pac Pac Pac 5 5 3 4 4 5 4 5 5 5 3 4 4 4 4 3 3 4 5 5 4 3 3 4 5 5 5 3 4 4 5 4 3 4 5 5 4 4 5 2 5 4 5 5 5 4 4 4 4 4 3 4 4 3 3 4 4 4 4 3 5 4 4 4 4 5 5 5 4 5 4 4 3 5 4 5 5 4 5 5 4 5 3 5 3 4 4 4 5 4 4 5 4 3 4 1 4 5 2 3 4 5 4 4 3 1 4 5 4 5 1 5 5 5 5 4 3 5 5 4 4 4 4 4 4 4 3 4 3 4 2 4 3 4 5 4 1 4 5 4 4 4 4 5 4 3 3 5 5 4 4 4 4 3 3 2 4 3 5 5 1 4 4 3 4 5 4 5 4 5 4 5 4 4 2 4 5 4 4 3 4 4 3 5 5 5 4 4 Pac Pac Pac Pac Pac Pac China China China China China China China China China China 5 4 5 4 3 5 5 5 4 4 4 4 4 3 3 2 4 4 5 2 4 4 5 5 4 4 4 4 4 4 4 3 5 4 4 3 4 4 4 4 3 3 3 3 3 3 2 2 4 4 5 3 4 5 4 3 3 3 2 3 2 3 2 1 Values Count of Quality Count of Ease of Use Count of Price Count of Service 10 10 10 10 30 30 30 30 100 100 100 100 10 10 10 10 50 50 50 50 200 200 200 200 7 23 96 9 9 27 90 2 23 66 1 22 89 0,7 2,3 9,6 0,9 0 0,9 2,7 9 0 0 0,2 2,3 6,6 0 0 0,1 2,2 8,9 0 0 Response times to customer service calls Q1 2013 4,36 5,42 5,50 2,79 5,55 3,65 8,02 4,00 3,34 4,92 3,55 3,52 1,25 2,18 4,35 2,46 2,07 2,90 2,58 5,50 2,47 4,24 1,88 4,25 5,08 4,40 1,64 6,40 3,68 3,92 4,13 3,34 3,28 3,24 3,25 5,20 5,28 4,33 4,64 2,65 3,42 3,97 1,26 Q2 2013 4,33 4,73 1,63 4,21 6,89 0,92 5,27 0,90 3,85 5,00 3,52 5,20 5,13 5,29 1,00 2,18 4,55 2,13 5,24 4,08 4,04 5,09 7,66 4,65 0,90 2,01 1,34 8,05 4,91 5,06 3,26 4,26 1,70 2,30 5,35 2,33 3,67 4,73 1,05 2,67 4,16 0,90 3,51 Q3 2013 3,71 2,52 2,69 3,47 5,12 1,00 3,44 6,04 2,53 2,39 3,26 4,68 3,59 1,07 2,86 4,44 4,87 6,76 2,84 1,25 3,43 2,98 4,65 2,66 4,99 3,76 3,12 2,12 4,32 3,61 4,02 2,63 4,47 4,18 4,73 2,65 2,36 3,64 5,62 0,90 6,40 3,21 3,55 Q4 2013 4,44 4,07 5,11 3,49 4,69 6,36 8,26 1,91 8,93 6,85 5,69 3,05 5,91 1,00 1,82 3,74 6,11 4,78 4,13 7,17 5,70 1,00 3,40 2,04 4,37 2,47 3,20 5,83 3,94 2,47 3,89 6,88 1,71 6,39 6,57 4,18 8,82 3,35 5,50 6,51 0,90 2,87 7,45 Q1 2014 2,75 3,24 4,35 5,58 2,89 5,09 2,33 1,69 3,88 3,39 5,14 0,98 2,34 2,80 3,06 2,40 1,59 3,05 1,50 5,58 3,11 1,08 3,63 1,86 1,90 6,07 1,00 1,00 1,19 3,79 5,86 0,90 2,24 0,90 3,87 2,46 3,84 2,43 1,54 0,90 3,69 1,73 3,52 Q2 2014 3,45 1,95 2,77 1,83 3,72 4,59 1,17 1,46 1,90 2,95 4,69 3,34 3,59 4,03 2,39 1,63 2,40 4,44 4,96 4,41 3,40 3,15 4,87 3,97 3,85 2,81 1,76 5,58 4,92 2,63 3,27 2,86 3,83 1,79 2,70 3,61 0,90 3,38 4,38 2,87 2,11 2,86 3,12 Q3 2014 1,67 2,58 3,47 3,12 1,00 5,40 3,90 4,49 2,06 4,49 3,57 3,41 3,31 2,79 2,09 4,28 4,47 1,94 3,90 3,32 2,20 3,52 2,31 1,00 5,90 1,09 4,60 3,52 4,14 4,13 2,43 2,34 2,53 4,14 2,65 3,21 3,85 2,20 4,57 2,99 4,19 3,03 1,90 Q4 2014 2,55 2,30 1,04 1,59 3,11 4,05 3,38 1,26 0,90 2,31 2,71 1,65 3,58 2,96 3,78 2,87 0,90 4,87 3,11 0,90 3,52 3,18 0,90 1,35 1,62 1,87 1,03 2,31 1,99 3,97 1,00 3,51 2,41 2,47 4,02 2,03 3,62 4,12 1,40 2,49 2,67 4,33 1,95 Colum 6,16 6,40 1,00 3,63 5,34 3,74 5,63 5,95 2,05 8,21 2,52 3,99 2,59 1,34 5,93 5,52 4,96 4,85 5,57 4,82 3,18 3,49 3,03 7,46 4,84 2,88 0,95 3,05 2,23 5,35 5,11 6,46 5,61 3,63 3,87 1,86 2,41 2,98 0,90 1,01 4,56 5,67 2,09 1,03 2,95 7,42 3,79 2,48 2,71 2,70 1,76 2,64 4,49 1,62 1,10 4,50 alpha = coefficient of confidenct 1-alpha = confidence level Column1 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level Alpha Margin of Error Lower Confidence Limit Upper Confidence Limit Margin of Error 3,915954 0,209586 3,828707 #N/A 1,481995 2,196311 0,093419 0,223205 7,019138 1 8,019138 195,7977 50 95% 5% 3,49 <--- fix this with formula 4,34 we are 95% confident that the call time will be between 3.49 and 4.34 #NUM! 3.49 and 4.34 Unit Tractor Transmission Costs two sample T test asume unequal Current $242,00 $176,00 $286,00 $269,00 $327,00 $264,00 $296,00 $333,00 $242,00 $288,00 $314,00 $302,00 $335,00 $242,00 $281,00 $289,00 $259,00 $322,00 $209,00 $282,00 $304,00 $391,00 $236,00 $383,00 $299,00 $300,00 $278,00 $303,00 $315,00 $321,00 Process A $242,00 $275,00 $199,00 $219,00 $273,00 $265,00 $435,00 $285,00 $384,00 $387,00 $299,00 $145,00 $266,00 $216,00 $331,00 $247,00 $280,00 $267,00 $210,00 $391,00 $297,00 $346,00 $230,00 $332,00 $301,00 $277,00 $336,00 $217,00 $274,00 $339,00 Process B $292,00 $321,00 $314,00 $242,00 $278,00 $300,00 $301,00 $286,00 $315,00 $300,00 $304,00 $300,00 $351,00 $277,00 $284,00 $276,00 $312,00 $273,00 $281,00 $303,00 $306,00 $312,00 $287,00 $306,00 $312,00 $295,00 $288,00 $313,00 $286,00 $338,00 Get the descriptive statistics If P value is > alpha than yo fail to reject b/c Ho becaus Column1 e T test asume unequal t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Variable 1 Variable 2 Mean 289,6 285,5 Variance 2061,145 4217,638 Observations 30 30 Hypothesized Mean Difference 0 df 52 t Stat 0,283405 P(T<=t) one-tail 0,388996 t Critical one-tail 1,674689 P(T<=t) two-tail 0,777992 pvalue RTT t Critical two-tail 2,006647 Variable 1 Variable 2 Mean 289,6 298,4333 Variance 2061,145 435,3575 Observations 30 30 Hypothesized Mean Difference 0 df 41 t Stat -0,96832 P(T<=t) one-tail 0,169281 t Critical one-tail 1,682878 P(T<=t) two-tail 0,338562 pvalue RTT t Critical two-tail 2,019541 If P value is > alpha than you fail to reject the null fail to reject b/c Ho because Pvalue=.38899 > alpha = .05 Column1 Column1 Column1 Mean 289,6 Standard Error 8,288838 Median 292,5 Mode 242 Standard Deviation 45,39983 Sample Variance 2061,145 Kurtosis 0,940711 Skewness -0,13171 Range 215 Minimum 176 Maximum 391 Sum 8688 Count 30 Mean 285,5 Standard Error 11,85698 Median 276 Mode #N/A Standard Deviation 64,94334 Sample Variance 4217,638 Kurtosis 0,048121 Skewness 0,280878 Range 290 Minimum 145 Maximum 435 Sum 8565 Count 30 Mean 298,4333 Standard Error 3,809451 Median 300 Mode 300 Standard Deviation 20,86522 Sample Variance 435,3575 Kurtosis 1,59724 Skewness -0,00885 Range 109 Minimum 242 Maximum 351 Sum 8953 Count 30 a: b: past knowledge variances are = if so, use the other "assuming equal variances" if you're not told this from past knowledge assume 'unequal variances' Mower Test Functional Performance 30 samples of size 100 Sample Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 1 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 Fail Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 5 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 6 Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 7 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 90 91 92 93 94 95 96 97 98 99 100 # of failures % of Failures/Sample Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 0,03 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 4 0,04 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 1 0,01 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 0 0 Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass 1 0,01 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 5 0,05 2 0,02 use formala 6.5 on pg 197 to calc the CV for an additional sample of 100 Mean fraction of the failures 0,018 "=phat" Sample Std Deviation 0,00242734 "=S-of-phat" Std Deve = sqrt( (phat)*(1-phat)/(n)) Degrees of Freedom 29 Prediction Interval 95% Alpha 5% n1 t #NAME? Formual Only exists in Excel 2010 and 2013 Margin of Error = ME Lower Confidnce Limit Upper Confidence Limit 95% confident that the mean fraction of failures will be betw 8 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 9 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 10 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass 11 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 12 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 13 Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 14 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 15 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 16 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 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Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 1 0,01 Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass 0 0 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 0,02 Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass 2 0,02 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 0,03 small 'n' here should be the total sample set 0,002427 tion of failures will be between 0.013 and .023 for an additional same set Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 0,03 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 1 0,01 Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass 1 0,01 2 0,02 17 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass 18 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 19 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 20 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 21 Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 22 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 23 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 24 Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 25 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Fail Pass Pass Pass Pass Pass Pass 2 0,02 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 0,03 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 0,02 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 4 0,04 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 0,02 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 1 0,01 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 1 0,01 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 0,02 1 0,01 26 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 27 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 28 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 29 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 30 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 0 0 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail 2 0,02 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 1 0,01 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 0 0 2 0,02 Chapter 7 Summary 7.1: 2014 Customer Survey Anova: Single Factor (when using more than one data set) SUMMARY Groups Quality Ease of Use Price Service Count Sum 200 200 200 200 879 833 734 828 Average 4,395 4,165 3,67 4,14 Variance 0,581884422 0,610829146 1,13678392 0,794371859 pvalue = 1.079x10(-14) ANOVA Source of Variation Between Groups Within Groups Total SS df 55,505 621,65 3 796 677,155 799 MS 18,50166667 0,780967337 F 23,69070484 P-value 1,079E-14 7.2: On-Time Deliveries Please see tab "Ch7.2 - On Time Deliveries' for details 2010 2014 Total Deliveries 14.154 17.010 On time deliveries 13.942 16.851 Proportion on time 0,985021902 0,990652557 z Critical value p-value 0,005630655 6,05 1,64 7,42964E-10 <--- very close to zero, which is < alpha = 0.05 The proportion of on-time deliveries in 2014 was 0.99065, representing a 0.00563 improvement over the 2010 proporti Because the p-value of approximately 0 is less than alpha (0.05), we can reject the Null Hypothesis. Thus, we cannot con Furthermore, z of 6.05 is greater than the critical value of 1.64, which also indicates that we can reject the Null Hypothe Since at least one of the means is different across the data sets, we can rejet the Null Hypothesis. This is furhter supported by the p-value of close to zero, which is less than alpha (0.05). ue = 1.079x10(-14) pretty much zero F crit 2,616088979 over the 2010 proportion of 0.98502. sis. Thus, we cannot conclude that on-time deliveries has significantly improved. reject the Null Hypothesis. Thus, we cannot conclude that on-time deliveries have significantly improved. 2014 Customer Survey Region NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA Quality Ease of UsePrice 4 4 4 5 5 5 5 5 4 4 4 5 5 4 5 5 5 5 4 4 4 4 5 5 5 5 5 4 5 5 5 4 4 5 5 5 5 5 4 5 5 5 5 1 4 5 4 4 5 4 5 4 5 5 5 4 5 4 5 4 4 5 4 4 3 5 3 4 5 5 4 4 1 4 5 4 3 5 4 5 5 3 4 4 5 4 Service 3 4 4 4 5 3 4 4 4 4 1 4 3 4 3 2 2 2 4 5 2 3 2 4 4 2 5 5 4 5 3 1 3 4 2 4 4 4 3 4 3 1 5 4 5 3 4 4 5 2 5 5 5 4 4 3 4 5 5 5 5 4 4 4 4 5 3 5 5 3 4 4 5 5 4 5 4 4 4 4 5 5 3 4 5 4 Mean Quality Mean Ease of Use Mean Price Mean Service 4,395 4,165 3,67 4,14 Since the means are different between the attributes, w p-Value 1,079E-14 Anova: Single Factor (when using more than one data se SUMMARY Groups Quality Ease of Use Price Service ANOVA Source of Variation Between Groups Within Groups Total Count 200 200 200 200 SS 55,505 621,65 677,155 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 5 5 5 5 5 5 5 5 5 5 4 5 5 5 4 5 4 5 5 5 5 4 4 5 5 5 5 5 5 5 5 5 4 3 5 4 3 1 4 5 4 5 5 4 5 5 4 4 5 5 4 4 4 4 4 5 4 3 4 5 5 4 4 5 5 5 4 4 4 4 4 4 4 5 4 4 3 4 4 5 5 5 4 2 4 5 5 5 5 5 2 4 4 3 2 4 3 4 4 4 1 5 3 4 5 4 5 4 4 5 5 5 3 4 5 5 4 4 3 5 4 4 5 4 5 1 3 2 4 3 4 3 3 4 5 4 4 4 5 5 4 4 5 4 4 4 5 4 5 4 5 5 4 5 5 4 5 4 4 5 4 2 5 5 4 5 4 5 4 2 5 5 5 5 5 4 5 5 4 5 4 5 5 4 5 4 4 NA NA NA NA NA NA NA NA NA NA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA 5 5 4 5 4 5 4 5 4 4 5 5 5 4 5 4 5 4 4 4 5 3 5 5 4 4 1 5 4 4 5 4 4 3 5 4 4 4 4 4 5 4 5 5 4 4 5 5 5 5 5 4 5 5 5 5 5 4 4 4 2 4 5 4 5 4 4 4 3 4 4 4 4 5 4 4 4 4 4 4 3 4 4 5 1 5 4 4 4 5 5 4 4 4 4 5 5 4 5 3 2 5 4 5 3 2 5 4 4 2 4 3 4 2 3 5 3 2 3 3 3 2 4 5 2 5 4 4 4 4 5 4 4 4 3 4 4 4 2 4 4 3 5 3 5 5 4 4 4 3 4 5 4 5 5 5 5 4 5 3 4 4 5 4 5 4 5 4 4 4 5 4 5 3 5 4 1 5 5 4 5 4 5 3 4 4 5 5 SA SA SA SA SA SA SA SA SA SA SA SA SA Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Pac Pac Pac Pac 5 5 3 4 4 5 4 5 5 5 3 4 4 4 4 3 3 4 5 5 4 3 3 4 5 5 5 3 4 4 5 4 3 4 5 5 4 4 5 2 5 4 5 5 5 4 4 4 4 4 3 4 4 3 3 4 4 4 4 3 5 4 4 4 4 5 5 5 4 5 4 4 3 5 4 5 5 4 5 5 4 5 3 5 3 4 4 4 5 4 4 5 4 3 4 1 4 5 2 3 4 5 4 4 3 1 4 5 4 5 1 5 5 5 5 4 3 5 5 4 4 4 4 4 4 4 3 4 3 4 2 4 3 4 5 4 1 4 5 4 4 4 4 5 4 3 3 5 5 4 4 4 4 3 3 2 4 3 5 5 1 4 4 3 4 5 4 5 4 5 4 5 4 4 2 4 5 4 4 3 4 4 3 5 5 5 4 4 Pac Pac Pac Pac Pac Pac China China China China China China China China China China 5 4 5 4 3 5 5 5 4 4 4 4 4 3 3 2 4 4 5 2 4 4 5 5 4 4 4 4 4 4 4 3 5 4 4 3 4 4 4 4 3 3 3 3 3 3 2 2 4 4 5 3 4 5 4 3 3 3 2 3 2 3 2 1 ANOVA Null Hypothesis states all means are the same To reject the Null Hypothesis, at least on of the means is different fferent between the attributes, we can reject the Null Hypothesis <---- is very close to zero, which is less than alpha = 0.05 Therefore can reject the Null Hypothesis when using more than one data set) Sum Average 879 4,395 833 4,165 734 3,67 828 4,14 Variance 0,581884 0,610829 1,136784 0,794372 pvalue = 1.079x10(-14) df MS 3 18,50167 796 0,780967 799 F 23,6907 P-value F crit 1,079E-14 2,616089 pretty much zero On-Time Delivery Month Jan-10 Feb-10 Mar-10 Apr-10 May-10 Jun-10 Jul-10 Aug-10 Sep-10 Oct-10 Nov-10 Dec-10 Jan-11 Feb-11 Mar-11 Apr-11 May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11 Dec-11 Jan-12 Feb-12 Mar-12 Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12 Nov-12 Dec-12 Jan-13 Feb-13 Mar-13 Apr-13 May-13 Jun-13 Jul-13 Total deliveries On Time Proportion On Time 2010 14.154 13.942 0,9850219 Ho:P<= Ha:P> Alpha 0,9850219 0,9850219 0,05 P-hat Po Delta SQRT(Po*(1-Po)/n) 0,9906526 0,9850219 0,0056307 0,000931 Test Z statistic Critical Value Z p-value 6,05 1,6448536 7,43E-10 Number of Number deliveries OnPercent Time 1086 1101 1116 1216 1183 1176 1198 1205 1223 1209 1198 1243 1220 1241 1237 1258 1262 1227 1243 1281 1272 1295 1298 1318 1281 1320 1352 1336 1291 1342 1352 1377 1385 1356 1362 1349 1386 1358 1371 1362 1350 1381 1392 1069 1080 1089 1199 1168 1160 1181 1189 1210 1194 1180 1223 1201 1224 1217 1242 1246 1212 1227 1264 1254 1278 1281 1296 1264 1304 1334 1320 1276 1326 1337 1360 1368 1338 1346 1333 1371 1342 1356 1348 1338 1366 1378 98,4% 98,1% 97,6% 98,6% 98,7% 98,6% 98,6% 98,7% 98,9% 98,8% 98,5% 98,4% 98,4% 98,6% 98,4% 98,7% 98,7% 98,8% 98,7% 98,7% 98,6% 98,7% 98,7% 98,3% 98,7% 98,8% 98,7% 98,8% 98,8% 98,8% 98,9% 98,8% 98,8% 98,7% 98,8% 98,8% 98,9% 98,8% 98,9% 99,0% 99,1% 98,9% 99,0% Since p-value is less than alpha (0.05) we can reject the N Since Z statistic is > critical value, we can reject the Null Aug-13 Sep-13 Oct-13 Nov-13 Dec-13 Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 1371 1402 1384 1399 1369 1401 1388 1395 1412 1403 1415 1426 1431 1445 1425 1413 1456 1359 1387 1370 1377 1357 1390 1376 1385 1401 1392 1402 1415 1420 1426 1414 1403 1427 99,1% 98,9% 99,0% 98,4% 99,1% 99,2% 99,1% 99,3% 99,2% 99,2% 99,1% 99,2% 99,2% 98,7% 99,2% 99,3% 98,0% 2014 17.010 16.851 0,9906526 <--- very close to zero, which is < alpha = 0.05 n alpha (0.05) we can reject the Null Hypothesis cal value, we can reject the Null Hypothesis Defects After Delivery Defects per million items received from suppliers Month 2010 2011 2012 2013 January February March April May June July August September October November December 812 810 813 823 832 848 837 831 827 838 826 819 828 832 847 839 832 840 849 857 839 842 828 816 824 836 818 825 804 812 806 798 804 713 705 686 682 695 692 686 673 681 696 688 671 645 617 603 2014 571 575 547 542 532 496 472 460 441 445 438 436 900 800 700 600 500 400 300 200 100 0 1 Average Month January February March April May June July August September October November December Average 826,3333 837,4167 785,9167 669,0833 2010 2014 812 810 813 823 832 848 837 831 827 838 826 819 571 575 547 542 532 496 472 460 441 445 438 436 826,3333 496,25 2 496,25 Two tail test because comparing one vs. other whenever you see word "change" ie from 2010 to 2-14 If Pvalue is less than alpha you reject the null therefore there is a sig so 2014 is statistically different than 2010 Series1 2 3 4 5 ect the null therefore there is a significant difference between the rates Unit Tractor Transmission Costs Current $242,00 $176,00 $286,00 $269,00 $327,00 $264,00 $296,00 $333,00 $242,00 $288,00 $314,00 $302,00 $335,00 $242,00 $281,00 $289,00 $259,00 $322,00 $209,00 $282,00 $304,00 $391,00 $236,00 $383,00 $299,00 $300,00 $278,00 $303,00 $315,00 $321,00 Process A Process B $242,00 $275,00 $199,00 $219,00 $273,00 $265,00 $435,00 $285,00 $384,00 $387,00 $299,00 $145,00 $266,00 $216,00 $331,00 $247,00 $280,00 $267,00 $210,00 $391,00 $297,00 $346,00 $230,00 $332,00 $301,00 $277,00 $336,00 $217,00 $274,00 $339,00 $292,00 $321,00 $314,00 $242,00 $278,00 $300,00 $301,00 $286,00 $315,00 $300,00 $304,00 $300,00 $351,00 $277,00 $284,00 $276,00 $312,00 $273,00 $281,00 $303,00 $306,00 $312,00 $287,00 $306,00 $312,00 $295,00 $288,00 $313,00 $286,00 $338,00 Right tail test RTT t test gives us the pvalue one tail test pval = $0,39 if pval is greater than alpha, fail to reject the null therefore the process is not better than existing r than existing Employee Retention YearsPLEYrsEducation College GPA 10 10 10 10 9,6 8,5 8,4 8,4 8,2 7,9 7,6 7,5 7,5 7,2 6,8 6,5 6,3 6,2 5,9 5,8 5,4 5,1 4,8 4,7 4,5 4,3 4 3,9 3,7 3,7 3,7 3,5 3,4 2,5 1,8 1,5 0,9 0,8 0,7 0,3 18 16 18 18 16 16 17 16 18 15 13 13 16 15 16 16 13 16 13 18 16 17 14 16 13 16 17 16 16 15 16 14 16 13 16 15 16 18 13 18 3,01 2,78 3,15 3,86 2,58 2,96 3,56 2,64 3,43 2,75 2,95 2,50 2,86 2,38 3,47 3,10 2,98 2,71 2,95 3,36 2,75 2,48 2,76 3,12 2,96 2,80 3,57 3,00 2,86 3,19 3,50 2,84 3,13 1,75 2,98 2,13 2,79 3,15 1,84 3,79 Age Gender College Grad Local 33 25 26 24 25 23 35 23 32 34 28 23 24 23 27 26 21 23 20 25 24 32 28 25 23 25 24 26 23 24 23 21 24 22 25 22 23 26 22 24 F M M F F M M M F M M M M F F M M M F M M M M F M M M F M M F M M M M M F M F F Y Y Y Y Y Y Y Y Y N N N Y N Y Y N Y N Y Y Y N Y N Y Y Y Y N Y N Y N Y N Y Y N Y Y Y N Y Y Y Y Y Y Y Y Y Y Y Y Y Y N Y Y N N Y N Y N Y N N N N Y N N N N Y N N N Separate males from femails Male Years PLE Separate males from femails Fe
Reminders: Install the 'Data Analysis toolpack' add-in XLMINER will be used in weeks 4,5 Datasets are where?And how to get them.All the data files Parallels and the MAC people Where to call for tech support for XLMINER Parallels Bb How to submit the project. One per group with all names of the group. Where to submit the projects? Chapter5-Evans 2nd edition 1 Bernoulli distribution models the individual failures. That is because in each trial we have only one of two outcomes( PASS,FAIL) 2 0.018 Frequency Fail Proportion 54 0.018 Pass 2946 0.982 Total 3000 1 3 Binomial, n = 100; p = 0.018 Excel 2010/13 x f(x) 0 0.162610572 1 0.298064186 2 0.270443167 3 0.161935419 4 0.071980459 5 0.02533243 6 0.00735208 7 0.001809677 8 0.000385616 9 7.22539E-05 10 1.20521E-05 11 1.80748E-06 12 2.45722E-07 13 3.04891E-08 14 3.47294E-09 15 3.64977E-10 16 3.55406E-11 17 3.21897E-12 18 2.72072E-13 19 2.15231E-14 20 1.59779E-15 4 Average blade weigtht Standard deviation Excel 2007 0.162610572 0.298064186 0.270443167 0.161935419 0.071980459 0.02533243 0.00735208 0.001809677 0.000385616 7.22539E-05 1.20521E-05 1.80748E-06 2.45722E-07 3.04891E-08 3.47294E-09 3.64977E-10 3.55406E-11 3.21897E-12 2.72072E-13 2.15231E-14 1.59779E-15 4.99 0.11 Pass Fail Using the empirical rules, we might expect 95% of blade weights to fall within 4.99 +/- 2*0.11 Excel 2010/13 Excel 2007 5 P(weight < 5.20) = P(weight > 5.20) = 0.971874817 0.97187482 0.028125183 0.02812518 6 P(weight < 4.80) = 0.042059347 0.04205935 7 Total # of weights= actual number > 5.2 actual number < 4.8 Percentage = 350 7 8 4.29% Comparing this with the answe and 6 shows that the predicted using the normal distribution is larger. [ .07 > .0429) 8 The process is generally stable except for a clear spike in the middle 9 By computing z-scores for the observations, we see that observation 171 has a z-score of 8.04;observ observation 37 has a z-score of -3.3. Obs 171 is clearly and outlier, and the others might be consider Go to Blade Weight Spreadsheet 10 Bin More Frequency 4.8 8 4.85 16 4.9 46 4.95 64 5 55 5.05 71 5.1 48 5.15 26 5.2 9 7 The histogram appears to be approximately normal Using Analytic Solver Platform, the best fitted distribution is an "inverse Gaussian," which is not desc However, we see that the normal distribution is a very close fit also. within 4.99 +/- 2*0.11 omparing this with the answers to questions 5 Using (5)&(6) we get that P(X>5.2)+P(X<4.8)= nd 6 shows that the predicted percentage sing the normal distribution is somewhat rger. [ .07 > .0429) 71 has a z-score of 8.04;observation 172 has a score of 3.1; and the others might be considered as outliers also. 0.07018453 Sample Weight 1 4.88 2 4.92 3 5.02 4 4.97 5 5.00 6 4.99 7 4.86 8 5.07 9 5.04 10 4.87 11 4.77 12 5.14 13 5.04 14 5.00 15 4.88 16 4.91 17 5.09 18 4.97 19 4.98 20 5.07 21 5.03 22 5.12 23 5.08 24 4.86 25 5.11 26 4.92 27 5.18 28 4.93 29 5.12 30 5.08 31 4.75 32 4.99 33 5.00 34 4.91 35 5.18 36 4.95 37 4.63 38 4.89 39 5.11 40 5.05 41 5.03 42 5.02 43 4.96 44 5.04 45 4.93 46 5.06 47 5.07 48 5.00 49 5.03 50 5.00 51 4.95 52 4.99 53 5.02 54 4.90 55 5.10 56 5.01 57 4.84 58 5.01 59 4.88 60 4.97 61 4.97 62 5.06 63 5.06 64 5.04 65 4.87 66 5.00 67 5.03 68 5.02 69 5.02 70 5.06 71 5.21 72 5.09 73 4.97 74 5.01 75 4.90 76 4.89 77 4.93 78 5.16 79 5.02 80 5.01 81 5.10 82 5.03 83 5.07 84 4.92 85 5.08 86 4.96 87 4.74 88 4.91 89 5.12 90 5.00 91 4.93 92 4.88 93 4.88 94 4.81 95 5.16 96 5.03 97 4.87 98 5.09 99 4.94 100 5.08 101 4.97 102 5.23 103 5.12 104 5.09 105 5.12 106 4.93 107 4.79 108 5.10 109 5.12 110 4.86 111 5.00 112 4.94 113 4.95 114 4.95 115 4.87 116 5.09 117 4.94 118 5.01 119 5.04 120 5.05 121 5.05 122 4.97 123 4.96 124 4.96 125 4.99 126 5.04 127 4.91 128 5.19 129 5.03 130 4.99 131 5.12 132 4.97 133 4.88 134 5.07 135 5.01 136 4.89 137 4.95 138 5.09 139 5.09 140 4.89 141 4.93 142 4.85 143 5.03 144 4.92 145 5.09 146 4.99 147 4.92 148 4.87 149 4.90 150 5.02 151 5.21 152 5.02 153 4.9 154 5 155 5.16 156 5.03 157 4.96 158 5.04 159 4.98 160 5.07 161 5.02 162 5.08 163 4.85 164 4.9 165 4.97 166 5.09 167 4.89 168 4.87 169 5.01 170 4.97 171 5.87 172 5.33 173 5.11 174 5.07 175 4.93 176 4.99 177 5.04 178 5.14 179 5.09 180 5.06 181 4.85 182 4.93 183 5.04 184 5.09 185 5.07 186 4.99 187 5.01 188 4.88 189 4.93 190 5.1 191 4.94 192 4.88 193 4.89 194 4.89 195 4.85 196 4.82 197 5.02 198 4.9 199 4.73 200 5.04 201 5.07 202 4.81 203 5.04 204 5.03 205 5.01 206 5.14 207 5.12 208 4.89 209 4.91 210 4.97 211 4.98 212 5.01 213 5.01 214 5.09 215 4.93 216 5.04 217 5.11 218 5.07 219 4.95 220 4.86 221 5.13 222 4.95 223 5.22 224 4.81 225 4.91 226 4.95 227 4.94 228 4.81 229 5.11 230 4.81 231 4.97 232 5.07 233 5.03 234 4.81 235 4.95 236 4.89 237 5.08 238 4.93 239 4.99 240 4.94 241 5.13 242 5.02 243 5.07 244 4.82 245 5.03 246 4.85 247 4.89 248 4.82 249 5.18 250 5.02 251 5.05 252 4.88 253 5.08 254 4.98 255 5.02 256 4.99 257 5.02 258 5.03 259 5.02 260 5.07 261 4.95 262 4.95 263 4.94 264 5.12 265 5.08 266 4.91 267 4.96 268 4.96 269 4.94 270 5.19 271 4.91 272 5.01 273 4.93 274 5.05 275 4.96 276 4.92 277 4.95 278 5.08 279 4.97 280 5.04 281 4.94 282 4.98 283 5.03 284 5.05 285 4.91 286 5.09 287 5.21 288 4.87 289 5.02 290 4.81 291 4.96 292 5.06 293 4.86 294 4.96 295 4.99 296 4.94 297 5.06 298 4.95 299 5.02 300 5.01 301 5.04 302 5.01 303 5.02 304 5.03 305 5.18 306 5.08 307 5.14 308 4.92 309 4.97 310 4.92 311 5.14 312 4.92 313 5.03 314 4.98 315 4.76 316 4.94 317 4.92 318 4.91 319 4.96 320 5.02 321 5.13 322 5.13 323 4.92 324 4.98 325 4.89 326 4.88 327 5.11 328 5.11 329 5.08 330 5.03 331 4.94 332 4.88 333 4.91 334 4.86 335 4.89 336 4.91 337 4.87 338 4.93 339 5.14 340 4.87 341 4.98 342 4.88 343 4.88 344 5.01 345 4.93 346 4.93 347 4.99 348 4.91 349 4.96 350 4.78 4.8 4.85 4.9 4.95 5 5.05 5.1 5.15 5.2 More Frequency 8 16 46 64 55 71 48 26 9 7 Histogram 80 Frequency Bin 60 40 20 0 Bin Blade Weight Zscore Possible Outlier -1.01384 -0.64783 0.26719 -0.19032 0.08418 -0.00732 -1.19684 0.72469 0.45019 -1.10534 -2.02036 1.36521 0.45019 0.08418 -1.01384 -0.73933 0.9077 -0.19032 -0.09882 0.72469 0.35869 1.1822 0.8162 -1.19684 1.0907 -0.64783 1.73121 -0.55633 1.1822 0.8162 -2.20336 -0.00732 0.08418 -0.73933 1.73121 -0.37333 -3.30138 OUTLIER GO to A171 as well -0.92234 1.0907 0.54169 0.35869 0.26719 -0.28183 0.45019 -0.55633 0.63319 0.72469 0.08418 7.00 6.00 5.00 4.00 Weight 3.00 2.00 1.00 0.00 1 9 17 25 33 41 49 57 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Weight 4.88 4.92 5.02 4.97 5.00 4.99 4.86 5.07 5.04 4.87 4.77 5.14 5.04 5.00 4.88 4.91 5.09 4.97 4.98 5.07 5.03 5.12 5.08 4.86 5.11 4.92 5.18 4.93 5.12 5.08 4.75 4.99 5.00 4.91 5.18 4.95 4.63 4.89 5.11 5.05 5.03 5.02 4.96 5.04 4.93 5.06 5.07 5.00 1.Leave A3 empty 2.Select A3:B353 3.Insert-->Line-->2D Line 4.Select Plot Area,Click Layout Tab 5. Add X-axis label, Y-axis label 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 5.03 5.00 4.95 4.99 5.02 4.90 5.10 5.01 4.84 5.01 4.88 4.97 4.97 5.06 5.06 5.04 4.87 5.00 5.03 5.02 5.02 5.06 5.21 5.09 4.97 5.01 4.90 4.89 4.93 5.16 5.02 5.01 5.10 5.03 5.07 4.92 5.08 4.96 4.74 4.91 5.12 5.00 4.93 4.88 4.88 4.81 5.16 5.03 4.87 5.09 4.94 0.35869 0.08418 -0.37333 -0.00732 0.26719 -0.83084 0.9992 0.17568 -1.37985 0.17568 -1.01384 -0.19032 -0.19032 0.63319 0.63319 0.45019 -1.10534 0.08418 0.35869 0.26719 0.26719 0.63319 2.00572 0.9077 -0.19032 0.17568 -0.83084 -0.92234 -0.55633 1.54821 0.26719 0.17568 0.9992 0.35869 0.72469 -0.64783 0.8162 -0.28183 -2.29486 -0.73933 1.1822 0.08418 -0.55633 -1.01384 -1.01384 -1.65435 1.54821 0.35869 -1.10534 0.9077 -0.46483 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 5.08 4.97 5.23 5.12 5.09 5.12 4.93 4.79 5.10 5.12 4.86 5.00 4.94 4.95 4.95 4.87 5.09 4.94 5.01 5.04 5.05 5.05 4.97 4.96 4.96 4.99 5.04 4.91 5.19 5.03 4.99 5.12 4.97 4.88 5.07 5.01 4.89 4.95 5.09 5.09 4.89 4.93 4.85 5.03 4.92 5.09 4.99 4.92 4.87 4.90 5.02 0.8162 -0.19032 2.18872 1.1822 0.9077 1.1822 -0.55633 -1.83735 0.9992 1.1822 -1.19684 0.08418 -0.46483 -0.37333 -0.37333 -1.10534 0.9077 -0.46483 0.17568 0.45019 0.54169 0.54169 -0.19032 -0.28183 -0.28183 -0.00732 0.45019 -0.73933 1.82271 0.35869 -0.00732 1.1822 -0.19032 -1.01384 0.72469 0.17568 -0.92234 -0.37333 0.9077 0.9077 -0.92234 -0.55633 -1.28834 0.35869 -0.64783 0.9077 -0.00732 -0.64783 -1.10534 -0.83084 0.26719 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 5.21 5.02 4.9 5 5.16 5.03 4.96 5.04 4.98 5.07 5.02 5.08 4.85 4.9 4.97 5.09 4.89 4.87 5.01 4.97 5.87 5.33 5.11 5.07 4.93 4.99 5.04 5.14 5.09 5.06 4.85 4.93 5.04 5.09 5.07 4.99 5.01 4.88 4.93 5.1 4.94 4.88 4.89 4.89 4.85 4.82 5.02 4.9 4.73 5.04 5.07 2.00572 0.26719 -0.83084 0.08418 1.54821 0.35869 -0.28183 0.45019 -0.09882 0.72469 0.26719 0.8162 -1.28834 -0.83084 -0.19032 0.9077 -0.92234 -1.10534 0.17568 -0.19032 8.04483 OUTLIER 3.10374 OUTLIER 1.0907 0.72469 -0.55633 -0.00732 0.45019 1.36521 0.9077 0.63319 -1.28834 -0.55633 0.45019 0.9077 0.72469 -0.00732 0.17568 -1.01384 -0.55633 0.9992 -0.46483 -1.01384 -0.92234 -0.92234 -1.28834 -1.56285 0.26719 -0.83084 -2.38636 0.45019 0.72469 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 4.81 5.04 5.03 5.01 5.14 5.12 4.89 4.91 4.97 4.98 5.01 5.01 5.09 4.93 5.04 5.11 5.07 4.95 4.86 5.13 4.95 5.22 4.81 4.91 4.95 4.94 4.81 5.11 4.81 4.97 5.07 5.03 4.81 4.95 4.89 5.08 4.93 4.99 4.94 5.13 5.02 5.07 4.82 5.03 4.85 4.89 4.82 5.18 5.02 5.05 4.88 -1.65435 0.45019 0.35869 0.17568 1.36521 1.1822 -0.92234 -0.73933 -0.19032 -0.09882 0.17568 0.17568 0.9077 -0.55633 0.45019 1.0907 0.72469 -0.37333 -1.19684 1.2737 -0.37333 2.09722 -1.65435 -0.73933 -0.37333 -0.46483 -1.65435 1.0907 -1.65435 -0.19032 0.72469 0.35869 -1.65435 -0.37333 -0.92234 0.8162 -0.55633 -0.00732 -0.46483 1.2737 0.26719 0.72469 -1.56285 0.35869 -1.28834 -0.92234 -1.56285 1.73121 0.26719 0.54169 -1.01384 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 5.08 4.98 5.02 4.99 5.02 5.03 5.02 5.07 4.95 4.95 4.94 5.12 5.08 4.91 4.96 4.96 4.94 5.19 4.91 5.01 4.93 5.05 4.96 4.92 4.95 5.08 4.97 5.04 4.94 4.98 5.03 5.05 4.91 5.09 5.21 4.87 5.02 4.81 4.96 5.06 4.86 4.96 4.99 4.94 5.06 4.95 5.02 5.01 5.04 5.01 5.02 0.8162 -0.09882 0.26719 -0.00732 0.26719 0.35869 0.26719 0.72469 -0.37333 -0.37333 -0.46483 1.1822 0.8162 -0.73933 -0.28183 -0.28183 -0.46483 1.82271 -0.73933 0.17568 -0.55633 0.54169 -0.28183 -0.64783 -0.37333 0.8162 -0.19032 0.45019 -0.46483 -0.09882 0.35869 0.54169 -0.73933 0.9077 2.00572 -1.10534 0.26719 -1.65435 -0.28183 0.63319 -1.19684 -0.28183 -0.00732 -0.46483 0.63319 -0.37333 0.26719 0.17568 0.45019 0.17568 0.26719 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 5.03 5.18 5.08 5.14 4.92 4.97 4.92 5.14 4.92 5.03 4.98 4.76 4.94 4.92 4.91 4.96 5.02 5.13 5.13 4.92 4.98 4.89 4.88 5.11 5.11 5.08 5.03 4.94 4.88 4.91 4.86 4.89 4.91 4.87 4.93 5.14 4.87 4.98 4.88 4.88 5.01 4.93 4.93 4.99 4.91 4.96 4.78 0.35869 1.73121 0.8162 1.36521 -0.64783 -0.19032 -0.64783 1.36521 -0.64783 0.35869 -0.09882 -2.11186 -0.46483 -0.64783 -0.73933 -0.28183 0.26719 1.2737 1.2737 -0.64783 -0.09882 -0.92234 -1.01384 1.0907 1.0907 0.8162 0.35869 -0.46483 -1.01384 -0.73933 -1.19684 -0.92234 -0.73933 -1.10534 -0.55633 1.36521 -1.10534 -0.09882 -1.01384 -1.01384 0.17568 -0.55633 -0.55633 -0.00732 -0.73933 -0.28183 -1.92886 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169 177 185 193 201 209 217 225 233 241 249 257 265 273 281 289 297 305 313 321 329 337 345 average weight= 4.9908 Std Dev of weight= 0.10929 Weight Sample Weight Mower Test Functional Performance FrequencyProportion 54 2946 3000 Fail Pass Total 0.018 0.982 1 Sample Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 1 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 Fail Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 5 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 6 Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 7 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 8 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 97 98 99 100 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 9 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 10 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass 11 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 12 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 13 Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 14 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 15 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 16 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 17 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 18 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Fail Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 19 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail 20 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Fail 21 Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 22 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 23 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 24 Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 25 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 26 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 27 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 28 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail 29 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 30 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2014 Customer Survey Region NA NA NA NA NA NA NA NA NA NA NA NA Quality Ease of Use Price Service 4 1 3 4 4 4 4 5 4 5 4 3 5 4 4 4 5 4 5 4 5 5 3 5 5 4 4 2 5 5 4 5 4 4 4 5 4 5 4 5 4 5 1 4 5 5 4 4 Not part of table Element# Question 1: 1 2 3 4 5 6 7 8 9 10 11 12 1-a:Steps Find the count of responses for each region 1 Click anywhere in the table to the left 2 Insert-->PivotTable 3 4 5 Pivot Table of Counts by Region NA 5 4 3 3 13 Row Labels Count of QualityCount of Ease of Use NA 4 5 4 4 14 China 10 NA 5 4 3 5 15 Eur 30 30 NA 5 5 2 5 16 NA 100 100 NA 5 4 2 5 17 Pac 10 10 NA 5 4 2 5 18 SA 50 50 NA 4 5 4 4 19 Grand Total 200 200 NA 4 4 5 4 20 NA 4 4 2 4 21 NA 4 3 3 4 22 NA 5 5 2 5 23 1-b: Find the count of Scales with counts 4,5 NA 5 3 4 3 24 region count of 4's NA 5 4 4 5 25 NA NA 5 5 2 5 26 NA 5 5 5 3 27 NA 4 4 5 4 28 "Top box" survey responses: Scale levels 4 and 5 NA NA 5 5 4 1 4 5 4 5 29 30 Region NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 5 4 4 5 5 5 5 5 4 5 5 5 5 3 5 5 5 5 5 5 5 5 5 5 4 5 5 5 4 5 4 5 5 5 5 4 5 4 3 5 4 5 5 3 4 4 5 4 4 4 5 5 4 4 4 4 4 5 4 3 4 5 5 4 4 5 5 5 4 4 3 1 3 4 2 4 4 4 3 4 3 1 5 3 2 4 3 4 4 4 1 5 3 4 5 4 5 4 4 5 5 5 3 4 5 5 4 5 4 4 4 4 5 5 3 4 5 4 4 4 5 4 4 4 5 4 5 4 5 5 4 5 5 4 5 4 4 5 4 2 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 10 Count of 5's 30 66 Use Formula tab to find out where COUNTIF gets its values China Eur NA Pac SA Total Not a Pivot Table.Using COUNTIF by Region Quality Ease of Use 7 23 96 9 45 180 9 27 90 8 42 176 1-c: Calculate the OVERALL proportions .9=180/200 .88=176/200 Proportion of customers with "top box" ratings: Using Totals by characteristic(quality,ease of use,price,service) Region Total Quality 0.9 Ease of Use 0.88 The quality and ease of use attributes got the most "top box" ratings with 90% of customers in the survey rating quality and 88% rating ease of use. Service follows with 82% and price rated by only 65% of the customers, the lowes 1-d: Calculate the proportions BY Region Proportion of customers in each geographic region with "top box" ratings: Region China Quality 0.70 Ease of Use 0.90 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA 4 4 5 5 5 5 5 5 5 5 5 4 3 5 4 3 1 4 5 4 5 5 4 5 5 5 5 4 5 4 5 4 5 4 4 5 5 5 4 5 4 5 4 4 4 5 3 5 5 4 4 1 5 4 4 5 4 4 3 5 4 4 4 4 4 5 4 5 5 4 4 5 4 4 4 4 4 5 4 4 3 4 4 5 5 5 4 2 4 5 5 5 5 5 2 4 4 5 5 5 5 4 5 5 5 5 5 4 4 4 2 4 5 4 5 4 4 4 3 4 4 4 4 5 4 4 4 4 4 4 3 4 4 5 1 5 4 4 4 5 5 4 4 4 5 4 4 3 5 4 4 5 4 5 1 3 2 4 3 4 3 3 4 5 4 4 4 5 5 4 5 5 4 5 3 2 5 4 5 3 2 5 4 4 2 4 3 4 2 3 5 3 2 3 3 3 2 4 5 2 5 4 4 4 4 5 4 4 4 3 4 4 4 2 4 4 5 5 4 5 4 5 4 2 5 5 5 5 5 4 5 5 4 5 4 5 5 4 5 4 4 3 5 3 5 5 4 4 4 3 4 5 4 5 5 5 5 4 5 3 4 4 5 4 5 4 5 4 4 4 5 4 5 3 5 4 1 5 5 4 5 4 5 3 4 4 5 5 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Eur NA Pac SA 0.77 0.96 0.90 0.90 0.90 0.90 0.80 0.84 Observations:NA and SA rated price with less "top box" ratings compared to qua use, and service with proportions 0.66 and 0.6, respectively. All the attributes received the most "top box" ratings in Pacific alone with proportio 0.9,0.8,0.9 and 0.9, respectively. 90% of the EUropean customers in the survey rated ease of use with most "top b with quality,price and service also getting relatively good ratings. Service and price got the least ratings followed by price in China with proportions respectively. The proportions obtained above are the point estimates of the actual proportions customers, along with the geographic regions, with "top box" ratings for the comp SA SA SA SA SA SA SA SA SA SA SA SA SA Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Pac Pac Pac Pac Pac Pac Pac Pac Pac Pac China China China China China China China China China China 5 5 3 4 4 5 4 5 5 5 3 4 4 4 4 3 3 4 5 5 4 3 3 4 5 5 5 3 4 4 5 4 3 4 5 5 4 4 5 2 5 4 5 5 5 4 4 5 4 5 4 3 5 5 5 4 4 4 4 4 3 3 2 4 4 4 3 4 4 3 3 4 4 4 4 3 5 4 4 4 4 5 5 5 4 5 4 4 3 5 4 5 5 4 5 5 4 5 3 5 3 4 4 4 5 4 4 5 4 3 4 4 5 2 4 4 5 5 4 4 4 4 4 4 4 3 4 1 4 5 2 3 4 5 4 4 3 1 4 5 4 5 1 5 5 5 5 4 3 5 5 4 4 4 4 4 4 4 3 4 3 4 2 4 3 4 5 4 1 4 5 4 4 5 4 4 3 4 4 4 4 3 3 3 3 3 3 2 2 4 4 5 4 3 3 5 5 4 4 4 4 3 3 2 4 3 5 5 1 4 4 3 4 5 4 5 4 5 4 5 4 4 2 4 5 4 4 3 4 4 3 5 5 5 4 4 4 4 5 3 4 5 4 3 3 3 2 3 2 3 2 1 38 39 40 41 42 43 44 45 46 47 48 49 50 esponses for each region he table to the left e of Counts by Region Count of PriceCount of Service 10 10 30 30 100 100 10 10 50 50 200 200 Scales with counts 4,5 o find out where COUNTIF gets its values Hyperlink e.Using COUNTIF by Region Price Service 2 23 66 9 30 130 1 22 89 9 43 164 .65=130/200 .82=164/200 ox" ratings: Using Totals by ice,service) Price 0.65 Service 0.82 es got the most "top box" ratings with 90% of the ty and 88% rating ease of use. rated by only 65% of the customers, the lowest. geographic region with "top box" ratings: Price 0.20 Service 0.10 0.77 0.66 0.90 0.60 0.73 0.89 0.90 0.86 ce with less "top box" ratings compared to quality, ease of 66 and 0.6, respectively. "top box" ratings in Pacific alone with proportions the survey rated ease of use with most "top box" ratings etting relatively good ratings. gs followed by price in China with proportions 0.1 and 0.2 , e the point estimates of the actual proportions of all the PLE hic regions, with "top box" ratings for the company. 1) Datasheet: 2014 Customer Survey Row Labels China Eur NA Pac SA Grand Total Count of QualityCount of Ease of UseCount of Price Count of Service 10 10 10 10 30 30 30 30 100 100 100 100 10 10 10 10 50 50 50 50 200 200 200 200 "Top box" survey responses: Scale levels 4 and 5 Region China Eur NA Pac SA Total Quality Ease of Use 7 23 96 9 45 180 Price 9 27 90 8 42 176 Service 2 23 66 9 30 130 1 22 89 9 43 164 0.65 Service 0.82 Proportion of customers with "top box" ratings: Region Total Quality 0.9 Ease of Use 0.88 Price The quality and ease of use attributes got the most "top box" ratings with 90% of the customers in the survey rating quality and 88% rating ease of use. Service follows with 82% and price rated by only 65% of the customers, the lowest. Proportion of customers in each geographic region with "top box" ratings: Region Quality Ease of Use Price Service China 0.7 0.9 0.2 0.1 Eur 0.77 0.90 0.77 0.73 NA 0.96 0.9 0.66 0.89 Pac 0.9 0.8 0.9 0.9 SA 0.9 0.84 0.6 0.86 NA and SA rated price with less "top box" ratings compared to quality, ease of use, and service with proportions 0.6 All the attributes received the most "top box" ratings in Pacific alone with proportions 0.9, 0.8, 0.9, and 0.9, respectiv 90% of the European customers in the survey rated ease of use with most "top box" ratings with quality, price, and ratings.Service got the least ratings followed by price in China with proportions 0.1 and 0.2, respectively. The proportions obtained above are the Point Estimates of the actual proporitons of all the PLE customers,along wi box" ratings for the company. 2) Datasheet: Response Time Q1 2013 Sample Size Q2 2013 50 Q3 2013 50 Q4 2013 50 50 Sample Mean Sample Standard Deviation Confidence Level Alpha Margin of Error Lower Confidence Limit Upper Confidence Limit 3.92 1.482 3.73 1.916 3.75 1.399 4.45 2.119 95% 0.05 0.4212 3.49 4.34 95% 0.05 0.5445 3.18 4.27 95% 0.05 0.3976 3.35 4.14 95% 0.05 0.6021 3.85 5.06 PLE can give customers the above interval estimates for response times to customer service calls in each quarter. With 95% confidence, it can assure that the true mean response time in each quarter will fall in the above interval for each qu Datasheet: Transmission Costs 3) Current Sample Size Sample Mean Sample Standard Deviation Confidence Level Alpha Margin of Error Lower Confidence Limit Upper Confidence Limit Process A Process B 30 $289.60 $45.40 30 $285.50 $64.94 30 $298.43 $20.87 95% 0.05 16.95257621 $272.65 $306.55 95% 0.05 24.25024319 $261.25 $309.75 95% 0.05 7.79120178 $290.64 $306.22 All the confidence intervals overlap suggesting that there might be no significant difference in the mean transmission costs fo Therefore, it cannot be determined that one of the proposed processes is better than the current process. 4) Datasheet: Mower Test Trying to find the prediction interval here. Mean fraction of the failures 0.018 Standard deviation 0.0024 Prediction Interval Alpha n t Margin of Error Lower Confidence Limit Upper Confidence Limit 95% 0.05 30 2.045229642 0.005046539 0.013 0.023 5) Datasheet: Blade Weight Sampling distribution of the mean would be approximately normal Mean estimated to be 4.99 Standard error = 0.109288/sqrt(350) = 0.005842 Mean Stdev Std error 6) Datasheet: Blade Weight TTT=Two Tail test Sample Mean Sample Standard Deviation 4.99 0.11 4.99 0.10928756 0.005841666 Confidence Level Alpha z Sampling Error Sample size 95% 0.05 1.96 is Z(alpha/2) by TTT 0.2 2 0.1 5 Creating "Defined Names" in Excel ma Go to Formulas-->Define Names to cre Sample size= Here, the sample standard deviation from the initial sample of 350 blade weights is used as an estimate for the population sta To find a 95% confidence interval for the mean blade weight with a sampling error of at most 0.2, a new sample size of 2 blad If the sampling error is specified as 0.1, the sample size should be 5. Question Go to 6.1 See details in: Ch6-1-2014 Customer Survey nd service with proportions 0.66 and 0.6, respectively. s 0.9, 0.8, 0.9, and 0.9, respectively. ratings with quality, price, and service also getting relatively good nd 0.2, respectively. all the PLE customers,along with the geographic regions, with "top Q1 2014 Q2 2014 50 Q3 2014 50 Q4 2014 50 50 3.09 1.585 3.11 1.228 3.20 1.279 2.53 1.131 95% 0.05 0.4505 2.64 3.54 95% 0.05 0.3490 2.76 3.46 95% 0.05 0.3636 2.84 3.57 95% 0.05 0.3214 2.21 2.85 Question Go to 6.2 See details in Ch6-2-Response Time e calls in each quarter. ll in the above interval for each quarter. Question 6.3 Goto See details in Ch6-3-Tra Question Go to 6.4 See details in 'Ch6-4-Mo n the mean transmission costs for the current process and the two proposed processes. rrent process. Mean estimated to be 4.99 Standard error = 0.109288/sqrt(350) = 0.005842 Sampling distribution of the mean would be approxim ( By Central Limit Theorem=CLT) Sample Size is a lot higher than 30 than the CLT sta ing "Defined Names" in Excel makes for much easier to understand formulas Formulas-->Define Names to create/edit/delete "defined Names" 2 5 an estimate for the population standard deviation to obtain the required new sample size. st 0.2, a new sample size of 2 blade weights must be measured. Response times to customer service calls Q1 2013 Q2 2013 Q3 2013 Q4 2013 Q1 2014 Q2 2014 Q3 2014 Q4 2014 4.36 4.33 3.71 4.44 2.75 3.45 1.67 2.55 5.42 4.73 2.52 4.07 3.24 1.95 2.58 2.30 5.50 1.63 2.69 5.11 4.35 2.77 3.47 1.04 2.79 4.21 3.47 3.49 5.58 1.83 3.12 1.59 5.55 6.89 5.12 4.69 2.89 3.72 1.00 3.11 3.65 0.92 1.00 6.36 5.09 4.59 5.40 4.05 8.02 5.27 3.44 8.26 2.33 1.17 3.90 3.38 4.00 0.90 6.04 1.91 1.69 1.46 4.49 1.26 3.34 3.85 2.53 8.93 3.88 1.90 2.06 0.90 4.92 5.00 2.39 6.85 3.39 2.95 4.49 2.31 3.55 3.52 3.26 5.69 5.14 4.69 3.57 2.71 3.52 5.20 4.68 3.05 0.98 3.34 3.41 1.65 1.25 5.13 3.59 5.91 2.34 3.59 3.31 3.58 2.18 5.29 1.07 1.00 2.80 4.03 2.79 2.96 4.35 1.00 2.86 1.82 3.06 2.39 2.09 3.78 2.46 2.18 4.44 3.74 2.40 1.63 4.28 2.87 2.07 4.55 4.87 6.11 1.59 2.40 4.47 0.90 2.90 2.13 6.76 4.78 3.05 4.44 1.94 4.87 2.58 5.24 2.84 4.13 1.50 4.96 3.90 3.11 5.50 4.08 1.25 7.17 5.58 4.41 3.32 0.90 2.47 4.04 3.43 5.70 3.11 3.40 2.20 3.52 4.24 5.09 2.98 1.00 1.08 3.15 3.52 3.18 1.88 7.66 4.65 3.40 3.63 4.87 2.31 0.90 4.25 4.65 2.66 2.04 1.86 3.97 1.00 1.35 5.08 0.90 4.99 4.37 1.90 3.85 5.90 1.62 4.40 2.01 3.76 2.47 6.07 2.81 1.09 1.87 1.64 1.34 3.12 3.20 1.00 1.76 4.60 1.03 6.40 8.05 2.12 5.83 1.00 5.58 3.52 2.31 3.68 4.91 4.32 3.94 1.19 4.92 4.14 1.99 3.92 5.06 3.61 2.47 3.79 2.63 4.13 3.97 4.13 3.26 4.02 3.89 5.86 3.27 2.43 1.00 3.34 4.26 2.63 6.88 0.90 2.86 2.34 3.51 3.28 1.70 4.47 1.71 2.24 3.83 2.53 2.41 3.24 2.30 4.18 6.39 0.90 1.79 4.14 2.47 3.25 5.35 4.73 6.57 3.87 2.70 2.65 4.02 5.20 2.33 2.65 4.18 2.46 3.61 3.21 2.03 5.28 3.67 2.36 8.82 3.84 0.90 3.85 3.62 4.33 4.73 3.64 3.35 2.43 3.38 2.20 4.12 4.64 1.05 5.62 5.50 1.54 4.38 4.57 1.40 2.65 2.67 0.90 6.51 0.90 2.87 2.99 2.49 3.42 4.16 6.40 0.90 3.69 2.11 4.19 2.67 3.97 0.90 3.21 2.87 1.73 2.86 3.03 4.33 1.26 3.51 3.55 7.45 3.52 3.12 1.90 1.95 6.16 5.95 5.93 3.49 2.23 1.86 2.09 2.70 6.40 2.05 5.52 3.03 5.35 2.41 1.03 1.76 1.00 8.21 4.96 7.46 5.11 2.98 2.95 2.64 3.63 2.52 4.85 4.84 6.46 0.90 7.42 4.49 5.34 3.99 5.57 2.88 5.61 1.01 3.79 1.62 3.74 2.59 4.82 0.95 3.63 4.56 2.48 1.10 5.63 1.34 3.18 3.05 3.87 5.67 2.71 4.50 2) Datasheet: Response Time Question 2: Sample Size Sample Mean Sample Standard Deviation Confidence Level Alpha Margin of Error Lower Confidence Limit Upper Confidence Limit Q1 2013 Q2 2013 Q3 2013 Q4 2013 Q1 2014 Q2 2014 Q3 2014 Q4 2014 50 50 50 50 50 50 50 3.92 3.73 3.75 4.45 3.09 3.11 3.20 1.482 1.916 1.399 2.119 1.585 1.228 1.279 95% 0.05 0.4212 3.49 4.34 95% 0.05 0.5445 3.18 4.27 95% 0.05 0.3976 3.35 4.14 95% 0.05 0.6021 3.85 5.06 95% 0.05 0.4505 2.64 3.54 95% 0.05 0.3490 2.76 3.46 95% 0.05 0.3636 2.84 3.57 50 2.53 1.131 95% 0.05 0.3214 2.21 2.85 PLE can give customers the above interval estimates for response times to customer service calls in each quarter. With 95% confidence, it can assure that the true mean response time in each quarter will fall in the above interval for each quarter. Confident.t=ME=t(α/2 ,n-1)*(Sample Standard Deviation/ SQRT(n) ) where n=sample size A confidence interval is like a Two Tail Test.That is why we divide alpha by 2 CONFIDENCE.T(alpha,standard_deviation,size) returns the margin of error.Thus the Confidence Interval is the Sample mean(xbar)±Margin of Error Unit Tractor Transmission Costs Current $242.00 $176.00 $286.00 $269.00 $327.00 $264.00 $296.00 $333.00 $242.00 $288.00 $314.00 $302.00 $335.00 $242.00 $281.00 $289.00 $259.00 $322.00 $209.00 $282.00 $304.00 $391.00 $236.00 $383.00 $299.00 $300.00 $278.00 $303.00 $315.00 $321.00 Process A $242.00 $275.00 $199.00 $219.00 $273.00 $265.00 $435.00 $285.00 $384.00 $387.00 $299.00 $145.00 $266.00 $216.00 $331.00 $247.00 $280.00 $267.00 $210.00 $391.00 $297.00 $346.00 $230.00 $332.00 $301.00 $277.00 $336.00 $217.00 $274.00 $339.00 Process B $292.00 $321.00 $314.00 $242.00 $278.00 $300.00 $301.00 $286.00 $315.00 $300.00 $304.00 $300.00 $351.00 $277.00 $284.00 $276.00 $312.00 $273.00 $281.00 $303.00 $306.00 $312.00 $287.00 $306.00 $312.00 $295.00 $288.00 $313.00 $286.00 $338.00 Question 3: Datasheet: Transmission Costs Test1: Ha:μA≤μC Test2: Ha:μA>μC Current Sample Size Sample Mean Sample Standard Deviation Confidence Level Alpha Process A 30 30 30 $289.60 $285.50 $298.43 $45.40 $64.94 $20.87 95% 95% 95% 0.05 0.05 0.05 Margin of Error 16.95257621 Ha:μB≤μC Ha:μB>μC Process B 24.25024319 7.79120178 Lower Confidence Limit $272.65 $261.25 $290.64 Upper Confidence Limit $306.55 $309.75 $306.22 All the confidence intervals overlap suggesting that there might be no significant difference in the mean transmission costs for the current process and the two proposed processes. Therefore , it cannot be determined that one of the proposed processes is better than the current process. Right Tail Test ( fro the Alternative) Right Tail(from the Alternative) t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Current Process A Mean 289.6 285.5 Variance 2061.14 4217.64 Observations 30 30 Hypothesized Mean 0 Difference df 52 t Stat 0.2834 P(T<=t) one-tail 0.389 t Critical one-tail 1.67469 P(T<=t) two-tail 0.77799 t Critical two-tail 2.00665 Current Process B Mean 289.6 298.433 Variance 2061.14 435.357 Observations 30 30 Hypothesized Mean 0 Difference df 41 t Stat -0.9683 P(T<=t) one-tail 0.16928 t Critical one-tail 1.68288 P(T<=t) two-tail 0.33856 t Critical two-tail 2.01954 Decision: Fail to reject Ho because pvalue>= alpha=.05 Decision: Fail to Reject Null because pvalue>=apha=.05 OR use descriptive stats Current Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level(95.0%) Process A 289.6 Mean Process B 285.5 Mean Using the Dat a Analysis Toolpack Add-in:( Var1 is Current,Var2 is ProcessA) 298.433 8.288837529 Standard Error 11.8569782 Standard Error 3.80945 292.5 Median 242 Mode 276 Median #N/A Mode 300 300 45.3998329 Standard Deviation 64.943344 Standard Deviation 20.8652 2061.144828 Sample Variance4217.63793 Sample Variance 435.357 0.940710683 -0.131713053 215 176 391 8688 30 16.95257621 Kurtosis 0.04812069 Skewness 0.2808784 Range 290 Minimum 145 Maximum 435 Sum 8565 Count 30 Confidence Level(95.0%) 24.2502432 Kurtosis 1.59724 Skewness -0.0089 Range 109 Minimum 242 Maximum 351 Sum 8953 Count 30 Confidence Level(95.0%) 7.7912 Population Variances assumed Unequal. Mower Test Functional Performance Sample Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 1 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 Fail Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 5 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 6 Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass 99 Pass 100 Pass # of failures % of failures Pass Pass 3 0.03 Pass Pass 4 0.04 Pass Pass 1 0.01 Pass Pass 0 0.00 Pass Pass 1 0.01 5 0.05 b106:ae106 4) Datasheet: Mower Test Mean fraction of the failures Sample Standard deviation Degrees of Freedom Prediction Interval is 95% Alpha n t Margin of Error=ME Lower Confidence Limit Upper Confidence Limit Mean fraction of failures=( average(.03+.04+.01+…) Want the prediction interval for an addtl sample Here we are dealing with proportions 0.0180 "=phat" C112=p-hat Standard Deviation=SQRT( (phat)*(1-phat)/(n 0.002427 "=S-of-phat" 29.000 0.950 95% prediction interval 0.050 n= 3000 30.000 n=COUNTA(b5:ae104)= 2.045 Critical Value t value for the two tail region 0.005 "t*s*sqrt(1+[1/30])" 0.013 "=phat-ME" 0.023 "=phat+ME" Meaning of result: We are 95% Confident that the mean fraction be between .013 and .023 7 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 8 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 9 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 10 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass 11 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 0.02 Pass Pass 1 0.01 Pass Pass 0 0.00 phat= p hat g with proportions d Deviation=SQRT( (phat)*(1-phat)/(n) ) for the population of 3,000 elements for the population of 3,000 elements diction interval Size of an additional sample of mower tests NTA(b5:ae104)= Value t value for the two tail region CV Prediction Formula on page 197 " =CV*STDEV*SQRT(1+(1/n))" 95% Confident that the mean fraction of failures(p-hat) for the population will een .013 and .023 Pass Pass 2 0.02 2 0.02 12 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 13 Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 14 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 15 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 16 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 17 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 18 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 19 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 3 3 0.03 0.03 Formula 6.5 on page 197(Evans 2/e) Pass Pass 1 0.01 Pass Pass 1 0.01 Pass Pass 2 0.02 Pass Pass 2 0.02 Pass Pass 3 0.03 Please note that a proportion is a kind of an average or mean. A confidence Interval provides an estimate for a population parameter like mew or p or sigma A CI is associated with the Sampling distribution of a satistic( such as x-bar) A Prediction Interval is associated with the distribution of the Random Variable itself. Formula 6.5 on page 197(Evans 2/e) Note: as n gets larger the PI becomes the CI 2 0.02 20 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Fail Pass Pass 21 Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 22 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 23 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 24 Pass Pass Fail Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 25 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 26 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 27 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 28 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 29 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 4 0.04 Pass Pass 2 0.02 Pass Pass 1 0.01 Pass Pass 1 0.01 Pass Pass 2 0.02 Pass Pass 1 0.01 Pass Pass 0 0.00 Pass Fail 2 0.02 Pass Pass 1 0.01 0 0.00 30 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Fail Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass 2 0.02 Blade Weight Sample Sorted Weight 1 2 3 4 5 6 Weight 4.88 4.92 5.02 4.97 5.00 4.99 7 4.86 4.78 8 5.07 4.79 9 5.04 4.81 10 4.87 4.81 11 4.77 4.81 12 5.14 4.81 13 5.04 4.81 14 5.00 4.81 15 4.88 4.81 16 4.91 4.82 17 5.09 4.82 18 4.97 4.82 19 4.98 4.84 20 5.07 4.85 21 5.03 4.85 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 5.12 5.08 4.86 5.11 4.92 5.18 4.93 5.12 5.08 4.75 4.99 5.00 4.91 5.18 4.95 4.63 4.89 5.11 5.05 5.03 5.02 4.96 4.85 4.85 4.85 4.86 item 1: 4.86 item 2: 4.86 item 3: 4.86 4.86 4.86 4.87 4.87 4.87 4.87 4.87 4.87 4.87 4.87 4.87 4.88 4.88 4.88 4.88 4.63 4.73 4.74 4.75 4.76 4.77 Weight 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 5.04 4.93 5.06 5.07 5.00 5.03 5.00 4.95 4.99 5.02 4.90 5.10 5.01 4.84 5.01 4.88 4.97 4.97 5.06 5.06 5.04 4.87 5.00 5.03 5.02 5.02 5.06 5.21 5.09 4.97 5.01 4.90 4.89 4.93 5.16 5.02 5.01 5.10 5.03 5.07 4.92 5.08 4.96 4.74 4.91 5.12 5.00 4.93 4.88 4.88 4.81 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.88 4.89 4.89 4.89 4.89 4.89 4.89 4.89 4.89 4.89 4.89 4.89 4.89 4.90 4.90 4.90 4.9 4.9 4.9 4.91 4.91 4.91 4.91 4.91 4.91 4.91 4.91 4.91 4.91 4.91 4.91 4.91 4.92 4.92 4.92 4.92 4.92 4.92 4.92 4.92 4.92 4.92 4.92 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 5.16 5.03 4.87 5.09 4.94 5.08 4.97 5.23 5.12 5.09 5.12 4.93 4.79 5.10 5.12 4.86 5.00 4.94 4.95 4.95 4.87 5.09 4.94 5.01 5.04 5.05 5.05 4.97 4.96 4.96 4.99 5.04 4.91 5.19 5.03 4.99 5.12 4.97 4.88 5.07 5.01 4.89 4.95 5.09 5.09 4.89 4.93 4.85 5.03 4.92 5.09 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.93 4.94 4.94 4.94 4.94 4.94 4.94 4.94 4.94 4.94 4.94 4.94 4.94 4.95 4.95 4.95 4.95 4.95 4.95 4.95 4.95 4.95 4.95 4.95 4.95 4.95 4.96 4.96 4.96 4.96 4.96 4.96 4.96 4.96 4.96 4.96 4.96 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 4.99 4.92 4.87 4.90 5.02 5.21 5.02 4.9 5 5.16 5.03 4.96 5.04 4.98 5.07 5.02 5.08 4.85 4.9 4.97 5.09 4.89 4.87 5.01 4.97 5.87 5.33 5.11 5.07 4.93 4.99 5.04 5.14 5.09 5.06 4.85 4.93 5.04 5.09 5.07 4.99 5.01 4.88 4.93 5.1 4.94 4.88 4.89 4.89 4.85 4.82 4.96 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.98 4.98 4.98 4.98 4.98 4.98 4.98 4.98 4.99 4.99 4.99 4.99 4.99 4.99 4.99 4.99 4.99 4.99 4.99 4.99 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5 5.01 5.01 5.01 5.01 5.01 5.01 5.01 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 5.02 4.9 4.73 5.04 5.07 4.81 5.04 5.03 5.01 5.14 5.12 4.89 4.91 4.97 4.98 5.01 5.01 5.09 4.93 5.04 5.11 5.07 4.95 4.86 5.13 4.95 5.22 4.81 4.91 4.95 4.94 4.81 5.11 4.81 4.97 5.07 5.03 4.81 4.95 4.89 5.08 4.93 4.99 4.94 5.13 5.02 5.07 4.82 5.03 4.85 4.89 5.01 5.01 5.01 5.01 5.01 5.01 5.01 5.01 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.03 5.04 5.04 5.04 5.04 5.04 5.04 5.04 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 4.82 5.18 5.02 5.05 4.88 5.08 4.98 5.02 4.99 5.02 5.03 5.02 5.07 4.95 4.95 4.94 5.12 5.08 4.91 4.96 4.96 4.94 5.19 4.91 5.01 4.93 5.05 4.96 4.92 4.95 5.08 4.97 5.04 4.94 4.98 5.03 5.05 4.91 5.09 5.21 4.87 5.02 4.81 4.96 5.06 4.86 4.96 4.99 4.94 5.06 4.95 5.04 5.04 5.04 5.04 5.04 5.04 5.04 5.05 5.05 5.05 5.05 5.05 5.05 5.06 5.06 5.06 5.06 5.06 5.06 5.06 5.07 5.07 5.07 5.07 5.07 5.07 5.07 5.07 5.07 5.07 5.07 5.07 5.07 5.08 5.08 5.08 5.08 5.08 5.08 5.08 5.08 5.08 5.08 5.08 5.09 5.09 5.09 5.09 5.09 5.09 5.09 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 5.02 5.01 5.04 5.01 5.02 5.03 5.18 5.08 5.14 4.92 4.97 4.92 5.14 4.92 5.03 4.98 4.76 4.94 4.92 4.91 4.96 5.02 5.13 5.13 4.92 4.98 4.89 4.88 5.11 5.11 5.08 5.03 4.94 4.88 4.91 4.86 4.89 4.91 4.87 4.93 5.14 4.87 4.98 4.88 4.88 5.01 4.93 4.93 4.99 4.91 4.96 5.09 5.09 5.09 5.09 5.09 5.09 5.10 5.10 5.10 5.1 5.11 5.11 5.11 5.11 5.11 5.11 5.11 5.12 5.12 5.12 5.12 5.12 5.12 5.12 5.12 5.12 5.13 5.13 5.13 5.13 5.14 5.14 5.14 5.14 5.14 5.14 5.16 5.16 5.16 5.18 5.18 5.18 5.18 5.19 5.19 5.21 5.21 5.21 5.22 5.23 5.33 350 4.78 5.87 Mean Stdev Std error Sampling distribution of the mean would be approximately normal ( By Central Limit Theorem=CLT) Sample Size is a lot higher than 30 that the CLT states Mean estimated to be 4.99 Standard error = 0.109288/sqrt(350) = 0.005842 Get descriptive statistics(Data Analysis toolpack) 4.9908 0.10929 0.00584 Weight Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level(95.0%) 4.9908 0.00584 4.99 5.02 0.10929 0.01194 11.3785 1.42374 1.24 4.63 5.87 1746.78 350 0.01149 When the questions is What is the Sampling distribution of x-bar , we need to provide three items: The Expected Value of x-bar=E(x) Std deviation of x-bar The Sampling distribution of x-bar x-bar~N( 4.99, .005842) And we should really draw the Normal curve as well Histogram for the original data. Do a frequency histogram a. Sort the weights b.min= c.max d.Range e.Number of classes f.Class width= 4.63 5.87 1.24 7 I picked this number. You may pick some other value 0.17714 sqrt(350) is much higher than we like to use. Sampling distribution of the original data is not really Normal , but kind of leading in that directions 4.63 4.81 4.98 5.16 5.34 5.52 5.69 5.87 6.05 Bin Frequency 4.63 1 4.81 7 4.98 160 5.16 169 5.34 12 5.52 0 5.69 0 5.87 0 6.05 1 More 0 200 Frequency Bins 150 100 50 0 4.63 4.81 Data Analysis Histogram CLT though states that even though the Sampling distribution of the original data is NOT NORMAL as long as we pick samples of size n>30 , the Sampling Distrbution of x-bar we ALWAYS BE NORMAL y pick some other value we like to use. Histogram Frequency 4.81 4.98 5.16 5.34 5.52 5.69 5.87 6.05 More nal data is NOT NORMAL ar we ALWAYS BE NORMAL Bin C Chapter 7 2014 Customer Survey 1 Region Quality Ease of UsePrice Service Using ANOVA, we reject the null hypothesis that all ratings NA NA NA NA NA NA NA NA NA NA NA NA 4 4 4 5 5 5 5 5 4 4 4 5 1 4 5 4 4 5 4 5 4 5 5 5 3 4 4 4 5 3 4 4 4 4 1 4 4 5 3 4 4 5 2 5 5 5 4 4 NA 5 4 3 3 NA 4 5 4 4 NA 5 4 3 5 NA NA NA NA NA 5 5 5 4 4 5 4 4 5 4 2 2 2 4 5 5 5 5 4 4 NA NA NA NA NA NA NA NA NA NA 4 4 5 5 5 5 5 4 5 5 4 3 5 3 4 5 5 4 4 1 2 3 2 4 4 2 5 5 4 5 4 4 5 3 5 5 3 4 4 5 NA NA NA NA NA 5 4 4 5 5 4 5 4 3 5 3 1 3 4 2 5 4 5 4 4 NA NA NA 5 5 5 4 5 5 4 4 4 4 4 5 NA NA NA NA 4 5 5 5 3 4 4 5 3 4 3 1 5 3 4 5 The test is: Ho:µ1=µ2=µ3=µ4 Ha:At least one mean is different from the other µ1=Mean 'Quality' rating µ2=Mean 'Ease of Use' rating µ3=Mean 'Price' rating µ4=Mean 'Service' rating Make the decision: Using the p-value method:pvalue=0<=.05=α p-value=1.08E-10=0 We reject the Null Hypothesis a F*=23.6907≥Fcv=2.616089 Using the Critical Value Method: We reject the Null Hypothesis a Using ANOVA, we reject the null hypothesis that all ratings 2 2a.Green region is the input region of interest 2b.Data-->Data Analysis-->ANOVA Single factor 2c.Fill-in as in Figure 1 Anova: Single Factor SUMMARY Groups Quality Ease of Use Price Service ANOVA Source of Variation Between Groups Within Groups Count 200 200 200 200 SS 55.505 621.65 NA 5 4 5 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3 5 5 5 5 5 5 5 5 5 5 4 5 5 5 4 5 4 5 5 5 5 4 4 5 5 5 5 5 5 5 5 5 4 3 5 4 3 1 4 5 4 5 5 4 4 4 5 5 4 4 4 4 4 5 4 3 4 5 5 4 4 5 5 5 4 4 4 4 4 4 4 5 4 4 3 4 4 5 5 5 4 2 4 5 5 5 5 5 2 3 2 4 3 4 4 4 1 5 3 4 5 4 5 4 4 5 5 5 3 4 5 5 4 4 3 5 4 4 5 4 5 1 3 2 4 3 4 3 3 4 5 4 4 4 4 4 5 4 4 4 5 4 5 4 5 5 4 5 5 4 5 4 4 5 4 2 5 5 4 5 4 5 4 2 5 5 5 5 5 4 5 5 4 5 4 5 5 4 5 Total 677.155 NA NA NA NA NA NA NA NA NA NA NA NA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA 5 5 5 5 4 5 4 5 4 5 4 4 5 5 5 4 5 4 5 4 4 4 5 3 5 5 4 4 1 5 4 4 5 4 4 3 5 4 4 4 4 4 5 4 5 5 4 4 5 5 5 5 4 5 5 5 5 5 4 4 4 2 4 5 4 5 4 4 4 3 4 4 4 4 5 4 4 4 4 4 4 3 4 4 5 1 5 4 4 4 5 5 5 5 4 5 5 4 5 3 2 5 4 5 3 2 5 4 4 2 4 3 4 2 3 5 3 2 3 3 3 2 4 5 2 5 4 4 4 4 5 4 4 4 3 4 4 4 4 4 3 5 3 5 5 4 4 4 3 4 5 4 5 5 5 5 4 5 3 4 4 5 4 5 4 5 4 4 4 5 4 5 3 5 4 1 5 5 4 5 4 5 3 4 SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur Eur 4 4 5 5 5 3 4 4 5 4 5 5 5 3 4 4 4 4 3 3 4 5 5 4 3 3 4 5 5 5 3 4 4 5 4 3 4 5 5 4 4 5 2 5 4 5 4 4 4 4 4 4 3 4 4 3 3 4 4 4 4 3 5 4 4 4 4 5 5 5 4 5 4 4 3 5 4 5 5 4 5 5 4 5 3 5 3 4 4 4 5 4 2 4 4 4 1 4 5 2 3 4 5 4 4 3 1 4 5 4 5 1 5 5 5 5 4 3 5 5 4 4 4 4 4 4 4 3 4 3 4 2 4 3 4 5 4 1 4 5 5 4 4 5 4 3 3 5 5 4 4 4 4 3 3 2 4 3 5 5 1 4 4 3 4 5 4 5 4 5 4 5 4 4 2 4 5 4 4 3 4 4 3 5 Pac Pac Pac Pac Pac Pac Pac Pac Pac Pac China China China China China China China China China China 5 5 4 4 5 4 5 4 3 5 5 5 4 4 4 4 4 3 3 2 4 5 4 3 4 4 5 2 4 4 5 5 4 4 4 4 4 4 4 3 4 5 4 4 5 4 4 3 4 4 4 4 3 3 3 3 3 3 2 2 5 5 4 4 4 4 5 3 4 5 4 3 3 3 2 3 2 3 2 1 Go back to "Ch7-Case Answers" e null hypothesis that all ratings are the same; so at least one differs from the rest. fferent from the other pvalue=0<=.05=α We reject the Null Hypothesis and Accept the Alternative Fcv=2.616089 using the F distribution table ???????? F*=23.6907≥Fcv=2.616089 We reject the Null Hypothesis and Accept the Alternative e null hypothesis that all ratings are the same; so at least one differs from the rest. Figure 1: ut region of interest >ANOVA Single factor Sum Average 879 4.395 833 4.165 734 3.67 828 4.14 df Variance 0.5818844 0.6108291 1.1367839 0.7943719 MS F P-value 3 18.501667 23.690705 1.079E-14 796 0.7809673 Between Groups vs Within Groups F crit 2.616089 799 On-Time Delivery a.Calculating the 2010 on time delivery prop Original Data Month Number of deliveries Number On Time Percent on Time Jan-10 Feb-10 Mar-10 Apr-10 May-10 Jun-10 Jul-10 Aug-10 Sep-10 Oct-10 Nov-10 Dec-10 Jan-11 Feb-11 Mar-11 1086 1101 1116 1216 1183 1176 1198 1205 1223 1209 1198 1243 1220 1241 1237 1069 1080 1089 1199 1168 1160 1181 1189 1210 1194 1180 1223 1201 1224 1217 98.4% 98.1% 97.6% 98.6% 98.7% 98.6% 98.6% 98.7% 98.9% 98.8% 98.5% 98.4% 98.4% 98.6% 98.4% Apr-11 May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11 Dec-11 Jan-12 Feb-12 Mar-12 Apr-12 May-12 Jun-12 Jul-12 Aug-12 Sep-12 Oct-12 Nov-12 Dec-12 Jan-13 1258 1262 1227 1243 1281 1272 1295 1298 1318 1281 1320 1352 1336 1291 1342 1352 1377 1385 1356 1362 1349 1386 1242 1246 1212 1227 1264 1254 1278 1281 1296 1264 1304 1334 1320 1276 1326 1337 1360 1368 1338 1346 1333 1371 98.7% 98.7% 98.8% 98.7% 98.7% 98.6% 98.7% 98.7% 98.3% 98.7% 98.8% 98.7% 98.8% 98.8% 98.8% 98.9% 98.8% 98.8% 98.7% 98.8% 98.8% 98.9% 2010 total # of deliveries 14154 The proportion of on time deliveries in 2010 b.Setup of the Null (Ho) and Alternative Hy Ho:P≤ Ha:P> We may test the null hypothesis(Ho) that the p (the newer & alternate hypothesis Ha is p > 0. Here we have a RTT=Right Tail Test, and the c.The Sample we need to use is from year 20 2014 total # of deliveries 17010 The proportion of the on time deliveries in t d.Since we are using proportions, w we will use Z. As we know Z=(p_ha Feb-13 Mar-13 Apr-13 May-13 Jun-13 Jul-13 Aug-13 Sep-13 1358 1371 1362 1350 1381 1392 1371 1402 1342 1356 1348 1338 1366 1378 1359 1387 98.8% 98.9% 99.0% 99.1% 98.9% 99.0% 99.1% 98.9% ??????????????????????????????????????? P-hat= Po= n= Oct-13 1384 1370 99.0% Test Statistic Z*= Nov-13 Dec-13 Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 1399 1369 1401 1388 1395 1412 1403 1415 1426 1431 1445 1425 1413 1456 1377 1357 1390 1376 1385 1401 1392 1402 1415 1420 1426 1414 1403 1427 98.4% 99.1% 99.2% 99.1% 99.3% 99.2% 99.2% 99.1% 99.2% 99.2% 98.7% 99.2% 99.3% 98.0% ( p-hat - po)= SQRT[(Po)(1-Po)/n]= Critical value of Z= P-value= Decision: Method 1: Critical Value Method: Because Z*≥Z=1.645 then we will reject the method 2: P-Value Method: Our decision should always be one of: Rejec say the same thing, but initally we must use Go back to Ch7-Case Answers ng the 2010 on time delivery proportion Proportion of On time 2010 # deliveries Deliveries ontime in 2010 13942 0.9850 rtion of on time deliveries in 2010 was 0.9850 the Null (Ho) and Alternative Hypotheses(Ha) 0.9850 0.9850 Po=.9850 α=.05 is given/assumed st the null hypothesis(Ho) that the proportion of on time deliveries in 2014 > 0.985 to determine if it has improved & alternate hypothesis Ha is p > 0.985) ave a RTT=Right Tail Test, and therefore all of α is allocated in the upper tail. ple we need to use is from year 2014. Proportion of On time 2014 # deliveries Deliveries ontime in 2014 16851 0.9907 rtion of the on time deliveries in the 2014 sample is .9907=p-hat we are using proportions, we will use the Normal Distribution and that means that use Z. As we know Z=(p_hat - Po)/(Sp_hat) ???????????????????????????????????????????????????? 0.9907 16851/17010 0.9850 17010 0.0056 0.0009 6.045884221 1.645 NORM.S.INV(1-α) 7.42964E-10 1-NORM.S.DIST(6.045,true) basically p-value=0 Critical Value Method: *≥Z=1.645 then we will reject the Null and state that the proportion has significantly improved. P-Value Method: p-value=0≤.05======> Reject the Null on should always be one of: Reject the Null OR Fail to Reject the Null. There are other equivalent ways to me thing, but initally we must use one of these two. The proportion of on time deliveries in 2010 was 0.9850. We may test the null hypothesis that the proportion of on time deliveries in 2014 is > 0.985 to determine if it has improved (the a Sample used is from 2014:::The sample proportion for 2014 is 0.9907 Critical value = 1.645 ( see below for calculations) p-value = 0.5 see below for calculations) Therefore, we cannot conclude a significant improvement Jan-14 1401 1390 99.2% Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 1388 1395 1412 1403 1415 1426 1431 1445 1425 1413 1456 1376 1385 1401 1392 1402 1415 1420 1426 1414 1403 1427 99.1% 99.3% 99.2% 99.2% 99.1% 99.2% 99.2% 98.7% 99.2% 99.3% 98.0% add RTT graph here ine if it has improved (the alternate hypothesis is p > 0.985) A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 B C D E F G H I J K L M Go back to "Ch7 Case Answers" Defects After Delivery Defects per million items received from suppliers Month 2010 2011 2012 2013 January 812 828 824 682 February 810 832 836 695 March 813 847 818 692 April 823 839 825 686 May 832 832 804 673 June 848 840 812 681 July 837 849 806 696 August 831 857 798 688 September 827 839 804 671 October 838 842 713 645 November 826 828 705 617 December 819 816 686 603 Average 826.33 837.42 785.92 669.08 N O P Q Question 3:Have the data in the worksheet Defects After delivery changed significantly over the past 5 tears? 2014 571 575 547 542 532 496 472 460 441 445 438 436 496.25 a. Using the 5 averages (in blue) plot the Line Chart 1 2 3 4 900.00 Select the blue region Insert-->Charts-->Line-->Line with Markers Click on the plot area-->Layout-->Axis Titles Click on the plot area-->Layout-->Chart Title Average Defects permillion 800.00 700.00 600.00 500.00 Average Defects permillion 400.00 2010 Average Defects permillion 826.33 2011 837.42 2012 785.92 2013 669.08 2014 496.25 300.00 200.00 100.00 0.00 2010 b. Sample Data for the Test 2010 2014 812 571 810 575 813 547 823 542 832 532 848 496 837 472 831 460 827 441 838 445 826 438 819 436 2011 2012 2013 2014 We may test for differences between 2010 and 2014 (assuming the samples are the monthly data since we don't know the actual number of shipments). Setup of the Null,and Alternative Hypotheses Ho:µ1=µ2 Ha:µ1≠µ2 OR Ho:µ1-µ2=0 Ha:µ1-µ2≠0 µ1=2010 population mean number of defects µ2=2014 Population mean number of defects "t-Test: Two-Sample Assuming Unequal Variances",because we are not told that the variances are equal,based on knowledge about the past Use the Data Analysis Excel Toolpack: Data Tab-->Data Analysis-->t:Test: Two Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances 2010 2014 Mean 826.333333 496.25 Variance 135.333333 2940.02 Observations 12 12 Hypothesized Mean Difference 0 df 12 t Stat 20.6189486 P(T<=t) one-tail 4.8844E-11 t Critical one-tail 1.78228756 P(T<=t) two-tail 9.7688E-11 t Critical two-tail 2.17881283 We have a TTT because of the ≠ sign in Ha c. Make the decision. Method 1: Critical Value Method: Test Statistic t* = t Critical Value= Because t* ≥ t Critical Value 20.61894864 2.17881283 Decision is: Reject Ho and Accept Ha Decision is: Reject Ho and Accept Ha==> The test clearly shows a significant difference in the mean defect rates. Method 2: P-value Method p-value= α= 9.76883E-11 0.05 Because p-value≤α Decision is: Reject Ho and Accept Ha==> The test clearly shows a significant difference in the mean defect rates. R S T U V W Unit Tractor Transmission Costs Question 4: Current $242.00 $176.00 $286.00 $269.00 $327.00 $264.00 $296.00 $333.00 $242.00 $288.00 $314.00 $302.00 $335.00 $242.00 $281.00 $289.00 $259.00 $322.00 $209.00 $282.00 $304.00 $391.00 $236.00 $383.00 $299.00 $300.00 $278.00 $303.00 $315.00 $321.00 289.6 45.39983 Process A $242.00 $275.00 $199.00 $219.00 $273.00 $265.00 $435.00 $285.00 $384.00 $387.00 $299.00 $145.00 $266.00 $216.00 $331.00 $247.00 $280.00 $267.00 $210.00 $391.00 $297.00 $346.00 $230.00 $332.00 $301.00 $277.00 $336.00 $217.00 $274.00 $339.00 Process B $292.00 $321.00 $314.00 $242.00 $278.00 $300.00 $301.00 $286.00 $315.00 $300.00 $304.00 $300.00 $351.00 $277.00 $284.00 $276.00 $312.00 $273.00 $281.00 $303.00 $306.00 $312.00 $287.00 $306.00 $312.00 $295.00 $288.00 $313.00 $286.00 $338.00 a. a1 285.5 298.43333 AVG 64.943344 20.865222 STDEV a2 b. b1 b2 Go Back to 'Ch7-Case Answers' Although engineering has collected data on alternative process costs for building transmissions in the worksheet Transmis they reach a conclusion as to whether one of the proposed processes is better than the current process? First look at the impact of Process A, by comparing Current & Process A Setup of the Null,and Alternative Hypotheses Ho:µ1≤µ2 Ha:µ1>µ2 OR Ho:µ1-µ2≤0 Ha:µ1-µ2>0 µ1="Current" population mean Transmission Cost µ2="Process A" Population mean Transmission cost RTT=Right Tail test Here we are testing that the [ mean "Current" Transmission Cost is ≤ mean "Process A" Transmission Cost] OR [ mean "Process A" Transmission Cost ≥mean "Current" Transmission Cost ] "t-Test: Two-Sample Assuming Unequal Variances",because we are not told that the variances are equal,based on knowledge about the past Use the Data Analysis Excel Toolpack: Data Tab-->Data Analysis-->t:Test: Two Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Current Process A My Comments Mean 289.6 285.5 Variance 2061.1448 4217.6379 Observations 30 30 Hypothesized Mean Difference 0 df 52 t Stat 0.2834045 t* P(T<=t) one-tail 0.388996 pvalue t Critical one-tail 1.6746892 t CV P(T<=t) two-tail 0.777992 t Critical two-tail 2.0066468 invt(1-.025,52) Make the decision Method 1: Critical Value Method t* =.283405 t CV one tail=1.674689 Tinv(1-.05,52) Because t* is not in the rejection region , we Fail to Reject the Null. In other words we do not have enough evidence from the sample to conclude that Process A is better than the current process. Testing hypotheses that the mean cost has improved for one of the new processes, we cannot conclude a signficant improveme Method 2: Pvalue Method pvalue=.388996 α=.05 Because pvalue=.388996 > α=.05, again we fail to reject the Null. In other words , we do not have enough evidence from the sample to conclude that Process A is better than the current Process Next look at the impact of Process B, by comparing Current & Process B We will repeat the same steps as in (a) above Setup of the Null,and Alternative Hypotheses Ho:µ1≤µ2 Ha:µ1>µ2 OR Ho:µ1-µ2≤0 Ha:µ1-µ2>0 µ1="Current" population mean Transmission Cost µ2="Process B" Population mean Transmission cost RTT=Right Tail test Here we are testing that the [ mean "Current" Transmission Cost is ≤ mean "Process B" Transmission Cost] OR [ mean "Process B" Transmission Cost ≥mean "Current" Transmission Cost ] "t-Test: Two-Sample Assuming Unequal Variances",because we are not told that the variances are equal,based on knowledge about the past Use the Data Analysis Excel Toolpack: Data Tab-->Data Analysis-->t:Test: Two Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Current Process B Mean 289.6 298.43333 Variance 2061.1448 435.35747 Observations 30 30 Hypothesized Mean Difference 0 df 41 t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail -0.968321 0.1692809 1.682878 0.3385619 2.019541 Make the decision Method 1: Critical Value Method t* =-.968321 t CV one tail=1.682878 Because t* is not in the rejection region , we Fail to Reject the Null. In other words we do not have enough evidence from the sample to conclude that Process A is better than the current process. Testing hypotheses that the mean cost has improved for one of the new processes, we cannot conclude a signficant improveme Method 2: Pvalue Method pvalue=.1692809 α=.05 Because pvalue> α=.05, again we fail to reject the Null. In other words , we do not have enough evidence from the sample to conclude that Process A is better than the current Process 'Ch7-Case Answers' ssions in the worksheet Transmission Costs , why didn't urrent process? ean Transmission Cost mean Transmission cost es are equal,based on CV=Critical value not have enough ot conclude a signficant improvement. ot have enough ean Transmission Cost mean Transmission cost ces are equal,based on t-Test: Two-Sample Assuming Unequal Variances Current Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 289.6 2061.1448 30 0 41 -0.968321 0.1692809 1.682878 0.3385619 2.019541 not have enough ot conclude a signficant improvement. nough evidence from qual Variances Process B 298.43333 435.35747 30 1 Using ANOVA, we reject the null hypothesis that all ratings are the same; so at least one differs from the rest. Anova: Single Factor SUMMARY Groups Count Quality Ease of Use Price Service Sum 200 200 200 200 Average 879 833 734 828 4.395 4.165 3.67 4.14 Variance 0.58188 0.61083 1.13678 0.79437 For details see the "7.1-2014 Customer Survey" Spreadsheet ANOVA Source of Variation SS Between Groups Within Groups Total df MS 55.505 621.65 3 796 677.155 799 18.502 0.781 F 23.6907 P-value F crit 1E-14 2.6161 2 The proportion of on time deliveries in 2010 was 0.9850. We may test the null hypothesis that the proportion of on time deliveries in 2014 is > 0.985 to determine if it has improved (the alternate hypothesis is p > 0.985) The sample proportion for 2014 is 0.9907 z = (0.9907 - 0.985)/SQRT(.985*(1-0.985)/n) = 6.1159407 6.045884 Critical value = 1.645 p-value = 7.42964E-10 Therefore, we cannot conclude a significant improvement 3 See details in Ch7-2-On-Delivery How else could we have done this? Could we have used 2populations? A chart of the average number of defects by year shows a declining trend. 900.00 800.00 700.00 600.00 500.00 400.00 300.00 200.00 100.00 0.00 Series1 1 2 3 4 5 We may test for differences between 2010 and 2014 (assuming the samples are the monthly data since we don't know the actual number of shipments) For details go to "Ch7-3=Defects After Delivery" t-Test: Two-Sample Assuming Unequal Variances 2008 Mean 826.3333333 Variance 135.3333333 Observations 12 Hypothesized Mean Difference 0 df 12 t Stat 20.61894864 P(T<=t) one-tail 4.88441E-11 t Critical one-tail 1.782287556 P(T<=t) two-tail 9.76883E-11 t Critical two-tail 2.17881283 2012 How else could we have done this? One population? 496.25 2940.02273 12 The test clearly shows a significant difference in the mean defect rates. 4 Testing hypotheses that the mean cost has improved for one of the new processes, we cannot conclude a signficant improvement. Question 4.Although engineering has collected data on alternative process costs for building transmissions in the worksheet Transmission Costs , why didn't they reach a conclusion as to whether one of the proposed processes is better than the current process? t-Test: Two-Sample Assuming Unequal Variances Current Mean 289.6 Variance 2061.144828 Observations 30 Hypothesized Mean Difference 0 df 52 t Stat 0.283404509 P(T<=t) one-tail 0.388996025 t Critical one-tail 1.674689154 P(T<=t) two-tail 0.77799205 t Critical two-tail 2.006646805 Process A 285.5 4217.63793 30 Current vs Process A See details in the 'Ch7-4-Transmission Costs' Spreadsheet t-Test: Two-Sample Assuming Unequal Variances Current Mean 289.6 Variance 2061.144828 Observations 30 Hypothesized Mean Difference 0 df 41 t Stat -0.968320801 P(T<=t) one-tail 0.169280943 t Critical one-tail 1.682878002 P(T<=t) two-tail 0.338561887 t Critical two-tail 2.01954097 5 Process B 298.433333 435.357471 30 Current vs Process B Conduct two sample tests on mean years at PLE for each factor. Question 5: Are there differences in employee retention due to gender,college graduation status, ow whether the employee is from the local area in the data in the worksheet Employee retention? t-Test: Two-Sample Assuming Unequal Variances Female Mean 5.530769231 Variance 12.25064103 Observations 13 Hypothesized Mean Difference 0 df 18 t Stat -0.009174759 P(T<=t) one-tail 0.496390313 t Critical one-tail 1.734063607 P(T<=t) two-tail 0.992780627 t Critical two-tail 2.10092204 Male 5.54074074 6.4494302 27 When we see the word differences , it means that we will have a TTT(Two Tail Test) Males vs Females For detail see spreadsheet "Ch7-5-EmployeeRetention-Gender " CONCLUSION: NO SIGNIFICANT DIFFERENCE BY GENDER t-Test: Two-Sample Assuming Unequal Variances College Grad N Mean 4.892307692 Variance 5.819102564 Observations 13 Hypothesized Mean Difference 0 df 29 t Stat -1.078815194 P(T<=t) one-tail 0.144780886 t Critical one-tail 1.699127027 P(T<=t) two-tail 0.289561772 t Critical two-tail 2.045229642 College Grad Y 5.84814815 9.10951567 27 College Graduates vs No College Graduates For detail see spreadsheet "Ch7-5-EmpRetention-CollegeGrads" CONCLUSION: NO SIGNIFICANT DIFFERENCE BY COLLEGE GRAD STATUS t-Test: Two-Sample Assuming Unequal Variances Local N Mean 3.629411765 Variance 5.690955882 Observations 17 Hypothesized Mean Difference 0 df 34 t Stat -4.418641425 P(T<=t) one-tail 4.80512E-05 t Critical one-tail 1.690924255 P(T<=t) two-tail 9.61023E-05 t Critical two-tail 2.032244509 Local Y 6.94782609 5.2726087 23 CONCLUSION: SIGNIFICANT DIFFERENCE BY LOCAL AREA EMPLOYEES FROM THE LOCAL AREA HAVE GREATER RETENTION Locals vs Non-Locals For detail see spreadsheet "Ch7-EmpRetention-Locality" 7.1 Employee Retention : Males vs Females Population 1: Males Sample 1: Male YearsPLE Male 10 10 8.5 8.4 8.4 7.9 7.6 7.5 7.5 6.5 6.3 6.2 5.8 5.4 5.1 4.8 4.5 4.3 4 3.7 3.7 3.5 M M M M M M M M M M M M M M M M M M M M M M 3.4 M 2.5 M 1.8 M 1.5 M 0.8 M Population 2: Females Sample 2: Female YearsPLE Female 10 10 9.6 8.2 7.2 6.8 5.9 4.7 3.9 3.7 0.9 0.7 0.3 F F F F F F F F F F F F F Test Statistic=t* t Critical Value=tCV t* is inside [ -2.10092,2.10092] Method 2: P-value Met p-value = CONCLUSION: NO SIG Go Back to 'Ch7-Case Answers' a Setup the test Ho:μM=μF Ho:μM - μF =0 Ha:μM≠μF Ha:μM - μF ≠0 TTT b Draw the diagram c Data Analysis Toolpack-->Data-->Data Analysis-->t-Test: Two Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Male YrsPLE Mean 5.540740741 Variance 6.449430199 Observations 27 Hypothesized Mean Difference 0 df 18 t Stat 0.009174759 P(T<=t) one-tail 0.496390313 t Critical one-tail 1.734063607 P(T<=t) two-tail 0.992780627 t Critical two-tail 2.10092204 d Female YearsPLE Unless told otherwise we will assume that the popula 5.530769231 The variances are Unequal based on knowledge from 12.25064103 13 is the pvalue for a LTT or RTT t Critical Value for a one Tail Test.If test is LTT then t C is the pvalue for a TTT t Critical Value for a one TTT Make the decision to reject Ho or Fail to reject Ho Method 1: Critical Value Method LCL= How Excel 2013 finds the Critical Values Lower Critical Value Test Statistic=t* t Critical Value=tCV UCV= Upper Critical Value and so we Fail To Reject the Null Ho 0.009174759 2.10092204 t* is inside [ -2.10092,2.10092] [ -2.10092,2.10092] is where we Fail To reject Ho Method 2: P-value Method( quickest to use) p-value = 0.992780627 > α= .05=alpha And so 0.05 CONCLUSION: NO SIGNIFICANT DIFFERENCE BY GENDER We Fail To Reject The Null Ho How Excel 2013 finds the pvalue for One Tail a If LTT,pvalue= If RTT,pvalue= If TTT ,pvalue= where x= Test Statistic=t* Cumulative=true μM = Average Years at PLE for Males μF = Average Years at PLE for Females le Assuming Unequal Variances we will assume that the population Variances are Unequal. qual based on knowledge from the Past. LTT=Left Tail Test,RTT=Right Tail Test e Tail Test.If test is LTT then t Critical one-tail=-1.73 013 finds the Critical Values -2.10092204 2.10092204 eject the Null Ho We Fail To Reject The Null Ho 013 finds the pvalue for One Tail and Two Tail Tests 0.496390313 0.496390313 0.992780627 st Statistic=t* CG=College Graduate 5.Employee Retention-College Graduates vs No College Graduates NCG=No College Graduae CG-YearsPLE No College Grad NCG-YearsPLE College Grad 0.7 N 0.3 Y 1.5 N 0.8 Y 2.5 N 0.9 Y 3.5 N 1.8 Y 3.7 N 3.4 Y 4.5 N 3.7 Y 4.8 N 3.7 Y 5.9 N 3.9 Y 6.3 N 4 Y 7.2 N 4.3 Y 7.5 N 4.7 Y 7.6 N 5.1 Y 7.9 N 5.4 Y 5.8 Y 6.2 Y 6.5 Y 6.8 Y 7.5 Y 8.2 Y 8.4 Y 8.4 Y 8.5 Y 9.6 Y 10 Y 10 Y 10 Y 10 Y CG=College Graduate Question 5: NCG=No College Graduae Are there differences in employee retention due to gender,college gra from the local area in the data in the worksheet Employee retention? t-Test: Two-Sample Assuming Unequal Variances CG-YearsPLE NCG-YearsPLE Mean 4.892307692 5.848148148 Variance 5.819102564 9.10951567 Observations 13 27 Hypothesized Mean Difference0 df 29 t Stat -1.078815194 P(T<=t) one-tail 0.144780886 t Critical one-tail 1.699127027 P(T<=t) two-tail 0.289561772 t Critical two-tail 2.045229642 CONCLUSION: NO SIGNIFICANT DIFFERENCE BY COLLEGE GRAD STATUS Follow same procedure as when dealing with Males vs Females e to gender,college graduation status, ow whether the employee is Employee retention? t-Test: Two-Sample Assuming Unequal Variances College GradCollege N Grad Y Mean 4.8923077 5.8481481 Variance 5.8191026 9.1095157 Observations 13 27 Hypothesized Mean Difference 0 df 29 t Stat -1.078815 P(T<=t) one-tail 0.1447809 t Critical one-tail 1.699127 P(T<=t) two-tail 0.2895618 t Critical two-tail 2.0452296 Same process as with Males College Grads vs vs Females No College Grads Employee Retention YearsPLE YrsEducation College GPA Age Gender College Grad Local 10 10 10 10 9.6 8.5 8.4 8.4 8.2 18 16 18 18 16 16 17 16 18 3.01 2.78 3.15 3.86 2.58 2.96 3.56 2.64 3.43 33 25 26 24 25 23 35 23 32 F M M F F M M M F Y Y Y Y Y Y Y Y Y Y Y N Y Y Y Y Y Y 7.9 7.6 7.5 7.5 7.2 6.8 6.5 6.3 6.2 5.9 5.8 15 13 13 16 15 16 16 13 16 13 18 2.75 2.95 2.50 2.86 2.38 3.47 3.10 2.98 2.71 2.95 3.36 34 28 23 24 23 27 26 21 23 20 25 M M M M F F M M M F M N N N Y N Y Y N Y N Y Y Y Y Y Y Y Y Y N Y Y 5.4 5.1 4.8 4.7 16 17 14 16 2.75 2.48 2.76 3.12 24 32 28 25 M M M F Y Y N Y N N Y N 4.5 4.3 4 3.9 3.7 3.7 3.7 3.5 3.4 2.5 1.8 13 16 17 16 16 15 16 14 16 13 16 2.96 2.80 3.57 3.00 2.86 3.19 3.50 2.84 3.13 1.75 2.98 23 25 24 26 23 24 23 21 24 22 25 M M M F M M F M M M M N Y Y Y Y N Y N Y N Y Y N Y N N N N Y N N N 1.5 0.9 0.8 0.7 15 16 18 13 2.13 2.79 3.15 1.84 22 23 26 22 M F M F N Y Y N N Y N N 0.3 18 3.79 24 F Y N Question 5: Are there differences in employee retention due to gender,college graduation status, ow whether the emplo from the local area in the data in the worksheet Employee retention? us, ow whether the employee is Conduct two sample tests on mean years at PLE for each factor. t-Test: Two-Sample Assuming Unequal Variances Female Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Male 5.5307692 5.5407407 12.250641 6.4494302 13 27 0 18 -0.009175 0.4963903 1.7340636 0.9927806 2.100922 3.5000916 CONCLUSION: NO SIGNIFICANT DIFFERENCE BY GENDER t-Test: Two-Sample Assuming Unequal Variances College GradCollege N Grad Y Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 4.8923077 5.8481481 5.8191026 9.1095157 13 27 0 29 -1.078815 0.1447809 1.699127 0.2895618 2.0452296 CONCLUSION: NO SIGNIFICANT DIFFERENCE BY COLLEGE GRAD STATUS t-Test: Two-Sample Assuming Unequal Variances Local N Mean Variance Local Y 3.6294118 6.9478261 5.6909559 5.2726087 Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 17 0 34 -4.418641 4.805E-05 1.6909243 9.61E-05 2.0322445 23 CONCLUSION: SIGNIFICANT DIFFERENCE BY LOCAL AREA EMPLOYEES FROM THE LOCAL AREA HAVE GREATER RETENTION 2.5395728

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