Business Statistics Help

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snazna

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K5.xls

K4.xls

K3.xlsx

K2.docx

K1.xls


Use the Student_Data.xls file which consists of 200 MBA students at Whatsamattu U. The file includes variables regarding students’ age, gender, major, GPA, Bachelors GPA, course load, English speaking status, family, weekly hours spent studying. Each of the three assigned problems should be formatted as a one page memo. Answers to all three of the problems should be submitted via the Drop Box as a single Word document with each of the problems clearly labeled. Be sure to include your name on the document itself!

COMPLETE PROBLEM 1: The battle of the sexes lives on still today. Since admission standards do not address gender there should be an equally diverse group of men and women in school, but do they perform equally well? Using the sample of 200 students, conduct a hypothesis test for two independent samples to determine if the mean GPA differs for men and women. Use a .05 significance level. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart (a bar chart or column chart will probably work best) comparing the means of the two groups. 

COMPLETE PROBLEM 2: You have heard that men are more likely than women to declare a major in an MBA program. Using the sample of 200 students (in the data file), conduct a hypothesis test of proportions to determine if the proportion of women with “no major” is greater than the proportion of men with “no major”. Use a .05 significance level. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart comparing the proportion of men without a major with the proportion of women without a major. 

COMPLETE PROBLEM 3: You have probably heard that if you want something done, give it to a busy person. So is one’s employment status a factor in their academic performance? Using the sample of 200 students (in the data file), conduct a hypothesis test using Analysis of Variance to determine if there is a difference in the mean GPA for those who are unemployed vs. work part-time vs. work full-time. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart comparing the means of the three groups. For this problem, a bar chart or column chart will work well; the display of the confidence intervals of the groups will also work.

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ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 17 18 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 Gender 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 Major Finance Finance Leadership Finance Finance Marketing Marketing Leadership Leadership Finance No Major No Major Finance Finance Finance Leadership Finance No Major Finance Leadership Leadership Finance Leadership Finance Leadership Finance Leadership Leadership Leadership Leadership Leadership Marketing Finance Leadership Finance Finance Leadership Leadership Leadership Finance Leadership Leadership Finance Leadership Finance Employ Full Time Full Time Unemployed Part Time Full Time Full Time Full Time Part Time Part Time Full Time Full Time Full Time Full Time Full Time Full Time Part Time Full Time Part Time Full Time Part Time Part Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Part Time Part Time Part Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Age 26 32 26 37 43 47 32 41 56 46 36 29 36 37 50 56 52 58 40 31 33 37 30 42 30 43 31 32 35 45 48 33 45 38 47 48 43 44 44 49 44 45 49 47 49 MBA_GPA 3,95 3,45 3,30 3,55 3,35 3,75 3,50 3,60 3,65 3,80 3,35 3,70 3,35 3,05 3,30 3,65 3,15 3,10 3,80 3,60 3,15 3,70 3,30 3,70 3,85 3,75 3,35 3,30 3,85 3,15 3,70 3,05 3,10 3,30 3,05 3,45 3,85 3,90 3,92 3,85 3,85 3,75 3,10 3,95 3,25 BS GPA Hrs_Studying 10 3,45 8 3,39 7 3,63 8 3,48 7 3,52 9 3,81 10 3,45 8 3,66 8 3,74 9 3,87 7 3,68 9 3,75 7 3,62 4 3,07 7 3,54 8 3,75 7 3,31 6 3,2 9 3,11 8 3,84 7 3,39 8 3,74 7 3,44 8 3,94 9 3,96 11 3,75 7 3,28 7 3,45 9 3,34 7 3,44 9 3,86 4 3,07 6 3,16 7 3,39 2 3,02 8 3,65 9 3,88 11 3,56 11 3,37 9 3,77 9 3,89 9 3,89 6 3,13 10 4 7 3,38 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 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 Leadership Finance Finance Leadership Leadership Leadership Leadership Marketing Marketing Marketing Leadership Leadership Leadership Leadership Leadership Marketing Marketing Leadership Marketing No Major Leadership Leadership Marketing Marketing Marketing Leadership Leadership Leadership Marketing Marketing Marketing Marketing Leadership Marketing Leadership Marketing Leadership Leadership Leadership Leadership Marketing Marketing Marketing Marketing Finance Leadership Marketing Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Unemployed Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time 48 52 59 29 49 49 52 45 47 52 30 27 38 33 37 27 29 44 53 50 46 47 33 34 35 47 48 48 35 35 36 37 50 41 53 43 55 58 61 34 44 29 45 45 32 42 32 3,60 3,60 3,10 3,35 3,96 3,65 3,90 3,40 3,40 3,10 3,80 3,60 3,74 3,10 3,65 3,40 3,85 3,20 3,15 3,97 3,80 3,10 3,93 3,91 3,70 3,05 3,75 3,80 3,95 3,65 3,90 3,45 3,80 3,80 3,55 3,80 3,45 3,80 3,45 3,90 3,65 3,95 3,60 3,85 3,50 3,40 3,60 3,63 3,66 3,21 3,38 3,65 3,87 3,88 3,7 3,66 3,19 3,87 3,56 3,44 3,14 3,66 3,68 3,91 3,43 3,23 3,01 3,81 3,11 3,76 3,84 3,78 3,13 3,69 3,86 3,65 3,92 3,87 3,77 3,87 3,78 3,75 3,93 3,71 3,95 3,58 3,97 3,81 3,99 3,6 3,93 3,6 3,43 3,78 8 11 6 7 11 8 9 8 8 6 9 11 10 6 8 8 9 7 7 11 9 5 11 10 9 5 9 9 10 8 9 8 9 9 8 9 8 9 8 11 8 10 8 9 8 8 8 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 120 121 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 Marketing Marketing No Major No Major No Major Marketing Marketing Marketing Marketing Marketing Leadership Leadership Leadership Marketing Marketing Marketing Marketing Marketing Marketing Marketing Marketing No Major Marketing Marketing Marketing No Major Finance Finance No Major No Major No Major No Major Marketing No Major No Major No Major No Major No Major No Major No Major No Major No Major Marketing Finance Finance Finance Finance Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Unemployed Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Unemployed Full Time Full Time Part Time Part Time 34 34 30 26 26 39 44 50 52 52 30 34 30 53 52 54 56 57 57 59 59 30 37 48 37 33 47 35 30 42 42 43 53 50 50 47 48 48 53 53 55 56 38 30 34 42 28 3,50 3,95 3,10 3,20 3,15 3,05 3,55 3,70 3,55 3,95 3,15 3,55 3,50 3,75 3,15 3,15 3,40 3,20 3,40 3,65 3,75 3,20 3,30 3,85 3,30 3,30 3,85 3,25 3,85 3,60 3,95 3,95 3,98 3,25 3,50 3,75 3,45 3,65 3,30 3,90 3,35 3,55 3,05 3,65 3,75 3,05 3,95 3,79 3,61 3,19 3,42 3,24 3,03 3,86 3,69 3,76 4 3,35 3,66 3,57 3,97 3,25 3,26 3,61 3,37 3,48 3,87 3,78 3,49 3,48 3,97 3,46 3,4 3,6 3,26 3,88 3,87 3,92 3,93 3,94 3,36 3,78 3,9 3,53 3,78 3,24 3,96 3,66 3,47 3,04 3,86 3,98 3,05 3,23 8 10 6 7 6 2 9 9 8 10 7 8 8 9 6 7 8 7 8 8 9 7 7 9 7 7 9 7 9 8 10 10 10 7 8 9 8 8 7 9 7 8 4 8 9 5 10 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 Finance Finance Finance Finance Finance Finance Finance Finance Leadership Leadership Leadership Finance Finance Leadership Leadership Leadership Leadership Leadership Leadership Leadership Finance Finance Leadership Finance Leadership Leadership Leadership Marketing Finance Finance No Major No Major No Major No Major Finance Finance Finance Marketing Marketing Marketing Marketing Marketing Leadership No Major No Major Finance Leadership Part Time Part Time Part Time Part Time Part Time Full Time Full Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Full Time Full Time Part Time Full Time Full Time Full Time Part Time Part Time Full Time Full Time Part Time Part Time Part Time Part Time Unemployed Unemployed Unemployed Part Time Part Time Part Time Part Time Part Time Unemployed Part Time Part Time Unemployed Unemployed 43 45 46 46 46 41 42 48 42 34 48 53 53 31 34 34 36 52 53 53 45 34 44 44 36 36 52 37 48 49 37 43 54 56 30 43 47 27 34 36 37 45 54 31 38 31 51 3,50 3,40 3,20 3,90 3,55 3,90 3,75 3,90 3,55 3,25 3,25 3,20 3,95 3,20 3,80 3,35 3,60 3,50 3,50 3,40 3,20 3,60 3,45 3,05 3,74 3,25 3,45 3,05 3,70 3,90 3,45 3,90 3,50 3,40 3,20 3,25 3,15 3,70 3,95 3,45 3,35 3,55 3,05 3,75 3,35 3,25 3,25 3,5 3,27 3,35 3,84 3,86 3,92 3,73 3,84 3,55 3,45 3,25 3,23 3,85 3,44 3,98 3,27 3,75 3,44 3,48 3,62 3,44 3,81 3,78 3,05 3,68 3,43 3,59 3,06 3,87 3,81 3,53 3,99 3,39 3,55 3,33 3,25 3,28 3,78 2,92 3,54 3,68 3,49 3,09 3,88 3,69 3,39 3,31 8 8 7 9 8 9 9 9 8 7 7 7 10 7 11 7 8 8 10 8 7 8 8 4 10 7 8 4 9 9 8 9 8 8 7 7 7 11 10 8 7 8 5 9 7 7 7 187 188 189 190 191 192 193 194 195 196 197 198 199 200 0 0 0 0 0 0 0 0 0 0 0 1 0 1 Finance Finance Marketing No Major Finance Leadership Marketing Marketing Marketing Leadership Marketing No Major Marketing No Major Unemployed Unemployed Unemployed Full Time Part Time Unemployed Unemployed Full Time Full Time Unemployed Unemployed Unemployed Unemployed Unemployed 36 40 45 59 27 49 32 30 31 55 27 54 42 30 3,55 3,20 3,15 3,65 3,50 3,40 3,70 3,94 3,70 3,30 3,35 3,10 3,25 3,10 3,71 3,44 3,29 3,86 3,65 3,28 3,89 3,21 3,83 3,54 3,58 3,18 3,42 3,15 8 7 7 8 8 8 9 11 9 7 7 5 7 6 Works FT 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 Variable descriptions Gender = 0 (female), 1 (male) Major = student's major Age = age of student in years MBA_GPA = overall GPA in the MBA program BS_GPA = overall GPA in the BS program Hrs_Studying = average hours studied per week Works FT = 0 (No), 1 (Yes) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 Unit 4 Practice Problems Practice Problem One Two Sample Hypothesis Test for the Mean (Independent Samples) Level of Significance 0.05 Sample Mean Sample Size Sample Standard Deviation No Pool 202763.158 38 33716.973 Standard Error (Computed) Test Statistic (Computed) 8037.41 -2.80 Pool 225258.065 62 46371.959 This is a two-tailed test since we are testing if the mean is different for the houses with vs. without a pool. The p-value of .0062 is less than .05, and so we reject the null hypothesis and conclude that the mean sales price for homes is different for houses with vs. without a pool. The fact that the sample mean is greater for houses with a pool indicates that houses with a pool likely have a higher mean price in the population. Two-Tailed Test  (  ) Lower Upper Crit Value Crit Value -1.9600 1.9600 pValue Decision 0.0062 Reject the null hypothesis Home Prices with and without Pool $230,000.00 $225,000.00 $220,000.00 $215,000.00 $210,000.00 $205,000.00 $200,000.00 $195,000.00 $190,000.00 No Pool Pool Unit 4 Practice Problems Practice Problem Two Two Sample Hypothesis Test for the Mean (Paired Samples) Level of Significance 0.05 Standard Error (Computed) Test Statistic (Computed) 3442.16 0.29 This is a two-tailed test since we are testing whether the mean appraisals given by the two agents are different from one another. The p-value of 0.7720 is greater than .05, and so we fail to reject the null hypothesis; there is insufficient evidence to conclude the mean appraisals are different for the two agents. As a result we conclude that the two agents’ appraisals are not significantly different from one another. Two-Tailed Test Lower Crit Value Upper Crit Value p-Value Decision -1.9842 1.9842 0.7720 Do not reject the null hypothesis  (d  ) (  ) Comparison of Two Agents' Appraisals $350,000 $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $0 1 11 21 31 41 Agent 1 51 61 Agent 2 71 81 91 Unit 4 Practice Problems Practice Problem Three Two Sample Hypothesis Test for the Proportion Level of Significance 0.05 Number of Successes Sample Size Brick 30 40 Wood or Stucco 32 60 Proportion (Computed) 0.75 0.53 Z Test Statistic (Computed) 2.19 This is an upper-tailed test since we are testing whether the proportion for brick homes with a pool is greater than that of wood & stucco homes with a pool. The p-value of .0144 is less than .05, and so we reject the null hypothesis. As a result, we conclude that brick homes are more likely to have a swimming pool than wood & stucco homes. Upper-Tail Test H1: (P1 > P2 or P2 < P1) Lower Crit Value Upper Crit Value pValue Decision n/a 1.6449 0.0144 Reject the null hypothesis Relationship between Construction Type and Pools 100% 80% Without Pool 60% With Pool 40% 20% 0% Brick Wood or Stucco Unit 4 Practice Problems Practice Problem Four Analysis of Variance SUMMARY Groups 2 BR 3 BR 4 BR 5 BR Count 24 26 26 24 Sum 4807000.000 5574000.000 5552000.000 5738000.000 ANOVA Source of Variation Treatment Error SS 18885182948.718 166271407051.282 df 3 96 Total 185156590000.000 99 Average 200291.667 214384.615 213538.462 239083.333 MS 6295060982.906 1731993823.451 Variance 1904911231.884 1205046153.846 1457058461.538 2430688405.797 F 3.635 F crit 2.699 The p-value of .0156 is less than .05, and so we reject the null hypothesis. Thus we conclude that a difference exists in the mean sales price based on number of bedrooms that a home has. Looking at the Post Hoc tests, we see that homes with 5 bedrooms are worth significantly more than homes with 2, 3 or 4 bedrooms. There doesn't appear to be a significant difference in mean prices for homes with 2, 3 or 4 bedrooms. Null hypothesis: Alternate hypothesis: Significance level: p-Value Decision:  =  =  =  Not all the means are equal 0.05 0.0156 Reject the null hypothesis Mean Differences Post-Hoc Tests Difference Comparison of Means 2 BR to 3 BR 2 BR to 4 BR 3 BR to 4 BR 2 BR to 5 BR 3 BR to 5 BR 4 BR to 5 BR 14092.949 13246.795 846.154 38791.667 24698.718 25544.872 Lower Conf. Limit -9291.274 -10137.428 -22065.612 14944.345 1314.495 2160.649 Upper Conf. Limit 37477.172 36631.018 23757.920 62638.989 48082.941 48929.095 Difference in Treatment Means??? - no difference - no difference - no difference ***Means are different*** ***Means are different*** ***Means are different*** Unit 4 Practice Problems Practice Problem Four (continued) Comparison of Number of Bedrooms and Home Price $240,000 $230,000 $220,000 $210,000 $200,000 $190,000 $180,000 2 BR 3 BR 4 BR 5 BR ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 17 18 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 Gender 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 Major Finance Finance Leadership Finance Finance Marketing Marketing Leadership Leadership Finance No Major No Major Finance Finance Finance Leadership Finance No Major Finance Leadership Leadership Finance Leadership Finance Leadership Finance Leadership Leadership Leadership Leadership Leadership Marketing Finance Leadership Finance Finance Leadership Leadership Leadership Finance Leadership Leadership Finance Leadership Finance Employ Full Time Full Time Unemployed Part Time Full Time Full Time Full Time Part Time Part Time Full Time Full Time Full Time Full Time Full Time Full Time Part Time Full Time Part Time Full Time Part Time Part Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Part Time Part Time Part Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Age 26 32 26 37 43 47 32 41 56 46 36 29 36 37 50 56 52 58 40 31 33 37 30 42 30 43 31 32 35 45 48 33 45 38 47 48 43 44 44 49 44 45 49 47 49 MBA_GPA 3.95 3.45 3.30 3.55 3.35 3.75 3.50 3.60 3.65 3.80 3.35 3.70 3.35 3.05 3.30 3.65 3.15 3.10 3.80 3.60 3.15 3.70 3.30 3.70 3.85 3.75 3.35 3.30 3.85 3.15 3.70 3.05 3.10 3.30 3.05 3.45 3.85 3.90 3.92 3.85 3.85 3.75 3.10 3.95 3.25 BS GPA Hrs_Studying 10 3.45 8 3.39 7 3.63 8 3.48 7 3.52 9 3.81 10 3.45 8 3.66 8 3.74 9 3.87 7 3.68 9 3.75 7 3.62 4 3.07 7 3.54 8 3.75 7 3.31 6 3.2 9 3.11 8 3.84 7 3.39 8 3.74 7 3.44 8 3.94 9 3.96 11 3.75 7 3.28 7 3.45 9 3.34 7 3.44 9 3.86 4 3.07 6 3.16 7 3.39 2 3.02 8 3.65 9 3.88 11 3.56 11 3.37 9 3.77 9 3.89 9 3.89 6 3.13 10 4 7 3.38 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 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 Leadership Finance Finance Leadership Leadership Leadership Leadership Marketing Marketing Marketing Leadership Leadership Leadership Leadership Leadership Marketing Marketing Leadership Marketing No Major Leadership Leadership Marketing Marketing Marketing Leadership Leadership Leadership Marketing Marketing Marketing Marketing Leadership Marketing Leadership Marketing Leadership Leadership Leadership Leadership Marketing Marketing Marketing Marketing Finance Leadership Marketing Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Unemployed Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time 48 52 59 29 49 49 52 45 47 52 30 27 38 33 37 27 29 44 53 50 46 47 33 34 35 47 48 48 35 35 36 37 50 41 53 43 55 58 61 34 44 29 45 45 32 42 32 3.60 3.60 3.10 3.35 3.96 3.65 3.90 3.40 3.40 3.10 3.80 3.60 3.74 3.10 3.65 3.40 3.85 3.20 3.15 3.97 3.80 3.10 3.93 3.91 3.70 3.05 3.75 3.80 3.95 3.65 3.90 3.45 3.80 3.80 3.55 3.80 3.45 3.80 3.45 3.90 3.65 3.95 3.60 3.85 3.50 3.40 3.60 3.63 3.66 3.21 3.38 3.65 3.87 3.88 3.7 3.66 3.19 3.87 3.56 3.44 3.14 3.66 3.68 3.91 3.43 3.23 3.01 3.81 3.11 3.76 3.84 3.78 3.13 3.69 3.86 3.65 3.92 3.87 3.77 3.87 3.78 3.75 3.93 3.71 3.95 3.58 3.97 3.81 3.99 3.6 3.93 3.6 3.43 3.78 8 11 6 7 11 8 9 8 8 6 9 11 10 6 8 8 9 7 7 11 9 5 11 10 9 5 9 9 10 8 9 8 9 9 8 9 8 9 8 11 8 10 8 9 8 8 8 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 120 121 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 Marketing Marketing No Major No Major No Major Marketing Marketing Marketing Marketing Marketing Leadership Leadership Leadership Marketing Marketing Marketing Marketing Marketing Marketing Marketing Marketing No Major Marketing Marketing Marketing No Major Finance Finance No Major No Major No Major No Major Marketing No Major No Major No Major No Major No Major No Major No Major No Major No Major Marketing Finance Finance Finance Finance Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Unemployed Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Full Time Unemployed Full Time Full Time Part Time Part Time 34 34 30 26 26 39 44 50 52 52 30 34 30 53 52 54 56 57 57 59 59 30 37 48 37 33 47 35 30 42 42 43 53 50 50 47 48 48 53 53 55 56 38 30 34 42 28 3.50 3.95 3.10 3.20 3.15 3.05 3.55 3.70 3.55 3.95 3.15 3.55 3.50 3.75 3.15 3.15 3.40 3.20 3.40 3.65 3.75 3.20 3.30 3.85 3.30 3.30 3.85 3.25 3.85 3.60 3.95 3.95 3.98 3.25 3.50 3.75 3.45 3.65 3.30 3.90 3.35 3.55 3.05 3.65 3.75 3.05 3.95 3.79 3.61 3.19 3.42 3.24 3.03 3.86 3.69 3.76 4 3.35 3.66 3.57 3.97 3.25 3.26 3.61 3.37 3.48 3.87 3.78 3.49 3.48 3.97 3.46 3.4 3.6 3.26 3.88 3.87 3.92 3.93 3.94 3.36 3.78 3.9 3.53 3.78 3.24 3.96 3.66 3.47 3.04 3.86 3.98 3.05 3.23 8 10 6 7 6 2 9 9 8 10 7 8 8 9 6 7 8 7 8 8 9 7 7 9 7 7 9 7 9 8 10 10 10 7 8 9 8 8 7 9 7 8 4 8 9 5 10 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 Finance Finance Finance Finance Finance Finance Finance Finance Leadership Leadership Leadership Finance Finance Leadership Leadership Leadership Leadership Leadership Leadership Leadership Finance Finance Leadership Finance Leadership Leadership Leadership Marketing Finance Finance No Major No Major No Major No Major Finance Finance Finance Marketing Marketing Marketing Marketing Marketing Leadership No Major No Major Finance Leadership Part Time Part Time Part Time Part Time Part Time Full Time Full Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Part Time Full Time Full Time Part Time Full Time Full Time Full Time Part Time Part Time Full Time Full Time Part Time Part Time Part Time Part Time Unemployed Unemployed Unemployed Part Time Part Time Part Time Part Time Part Time Unemployed Part Time Part Time Unemployed Unemployed 43 45 46 46 46 41 42 48 42 34 48 53 53 31 34 34 36 52 53 53 45 34 44 44 36 36 52 37 48 49 37 43 54 56 30 43 47 27 34 36 37 45 54 31 38 31 51 3.50 3.40 3.20 3.90 3.55 3.90 3.75 3.90 3.55 3.25 3.25 3.20 3.95 3.20 3.80 3.35 3.60 3.50 3.50 3.40 3.20 3.60 3.45 3.05 3.74 3.25 3.45 3.05 3.70 3.90 3.45 3.90 3.50 3.40 3.20 3.25 3.15 3.70 3.95 3.45 3.35 3.55 3.05 3.75 3.35 3.25 3.25 3.5 3.27 3.35 3.84 3.86 3.92 3.73 3.84 3.55 3.45 3.25 3.23 3.85 3.44 3.98 3.27 3.75 3.44 3.48 3.62 3.44 3.81 3.78 3.05 3.68 3.43 3.59 3.06 3.87 3.81 3.53 3.99 3.39 3.55 3.33 3.25 3.28 3.78 2.92 3.54 3.68 3.49 3.09 3.88 3.69 3.39 3.31 8 8 7 9 8 9 9 9 8 7 7 7 10 7 11 7 8 8 10 8 7 8 8 4 10 7 8 4 9 9 8 9 8 8 7 7 7 11 10 8 7 8 5 9 7 7 7 187 188 189 190 191 192 193 194 195 196 197 198 199 200 0 0 0 0 0 0 0 0 0 0 0 1 0 1 Finance Finance Marketing No Major Finance Leadership Marketing Marketing Marketing Leadership Marketing No Major Marketing No Major Unemployed Unemployed Unemployed Full Time Part Time Unemployed Unemployed Full Time Full Time Unemployed Unemployed Unemployed Unemployed Unemployed 36 40 45 59 27 49 32 30 31 55 27 54 42 30 3.55 3.20 3.15 3.65 3.50 3.40 3.70 3.94 3.70 3.30 3.35 3.10 3.25 3.10 3.71 3.44 3.29 3.86 3.65 3.28 3.89 3.21 3.83 3.54 3.58 3.18 3.42 3.15 8 7 7 8 8 8 9 11 9 7 7 5 7 6 Works FT 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 Variable descriptions Gender = 0 (female), 1 (male) Major = student's major Age = age of student in years MBA_GPA = overall GPA in the MBA program BS_GPA = overall GPA in the BS program Hrs_Studying = average hours studied per week Works FT = 0 (No), 1 (Yes) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 Unit 4 Practice Problems Practice Problem One Two Sample Hypothesis Test for the Mean (Independent Samples) Level of Significance 0.05 Sample Mean Sample Size Sample Standard Deviation No Pool 202763.158 38 33716.973 Standard Error (Computed) Test Statistic (Computed) 8037.41 -2.80 Pool 225258.065 62 46371.959 This is a two-tailed test since we are testing if the mean is different for the houses with vs. without a pool. The p-value of .0062 is less than .05, and so we reject the null hypothesis and conclude that the mean sales price for homes is different for houses with vs. without a pool. The fact that the sample mean is greater for houses with a pool indicates that houses with a pool likely have a higher mean price in the population. Two-Tailed Test  (  ) Lower Upper Crit Value Crit Value -1.9600 1.9600 pValue Decision 0.0062 Reject the null hypothesis Home Prices with and without Pool $230,000.00 $225,000.00 $220,000.00 $215,000.00 $210,000.00 $205,000.00 $200,000.00 $195,000.00 $190,000.00 No Pool Pool Unit 4 Practice Problems Practice Problem Two Two Sample Hypothesis Test for the Mean (Paired Samples) Level of Significance 0.05 Standard Error (Computed) Test Statistic (Computed) 3442.16 0.29 This is a two-tailed test since we are testing whether the mean appraisals given by the two agents are different from one another. The p-value of 0.7720 is greater than .05, and so we fail to reject the null hypothesis; there is insufficient evidence to conclude the mean appraisals are different for the two agents. As a result we conclude that the two agents’ appraisals are not significantly different from one another. Two-Tailed Test Lower Crit Value Upper Crit Value p-Value Decision -1.9842 1.9842 0.7720 Do not reject the null hypothesis  (d  ) (  ) Comparison of Two Agents' Appraisals $350,000 $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $0 1 11 21 31 41 Agent 1 51 61 Agent 2 71 81 91 Unit 4 Practice Problems Practice Problem Three Two Sample Hypothesis Test for the Proportion Level of Significance 0.05 Number of Successes Sample Size Brick 30 40 Wood or Stucco 32 60 Proportion (Computed) 0.75 0.53 Z Test Statistic (Computed) 2.19 This is an upper-tailed test since we are testing whether the proportion for brick homes with a pool is greater than that of wood & stucco homes with a pool. The p-value of .0144 is less than .05, and so we reject the null hypothesis. As a result, we conclude that brick homes are more likely to have a swimming pool than wood & stucco homes. Upper-Tail Test H1: (P1 > P2 or P2 < P1) Lower Crit Value Upper Crit Value pValue Decision n/a 1.6449 0.0144 Reject the null hypothesis Relationship between Construction Type and Pools 100% 80% Without Pool 60% With Pool 40% 20% 0% Brick Wood or Stucco Unit 4 Practice Problems Practice Problem Four Analysis of Variance SUMMARY Groups 2 BR 3 BR 4 BR 5 BR Count 24 26 26 24 Sum 4807000.000 5574000.000 5552000.000 5738000.000 ANOVA Source of Variation Treatment Error SS 18885182948.718 166271407051.282 df 3 96 Total 185156590000.000 99 Average 200291.667 214384.615 213538.462 239083.333 MS 6295060982.906 1731993823.451 Variance 1904911231.884 1205046153.846 1457058461.538 2430688405.797 F 3.635 F crit 2.699 The p-value of .0156 is less than .05, and so we reject the null hypothesis. Thus we conclude that a difference exists in the mean sales price based on number of bedrooms that a home has. Looking at the Post Hoc tests, we see that homes with 5 bedrooms are worth significantly more than homes with 2, 3 or 4 bedrooms. There doesn't appear to be a significant difference in mean prices for homes with 2, 3 or 4 bedrooms. Null hypothesis: Alternate hypothesis: Significance level: p-Value Decision:  =  =  =  Not all the means are equal 0.05 0.0156 Reject the null hypothesis Mean Differences Post-Hoc Tests Difference Comparison of Means 2 BR to 3 BR 2 BR to 4 BR 3 BR to 4 BR 2 BR to 5 BR 3 BR to 5 BR 4 BR to 5 BR 14092.949 13246.795 846.154 38791.667 24698.718 25544.872 Lower Conf. Limit -9291.274 -10137.428 -22065.612 14944.345 1314.495 2160.649 Upper Conf. Limit 37477.172 36631.018 23757.920 62638.989 48082.941 48929.095 Difference in Treatment Means??? - no difference - no difference - no difference ***Means are different*** ***Means are different*** ***Means are different*** Unit 4 Practice Problems Practice Problem Four (continued) Comparison of Number of Bedrooms and Home Price $240,000 $230,000 $220,000 $210,000 $200,000 $190,000 $180,000 2 BR 3 BR 4 BR 5 BR Two Sample Hypothesis Test for the Mean (Independent Samples) Level of Significance 0.05 Sample Mean Sample Size Sample Standard Deviation Group 1 100 30 10 Standard Error (Computed) Test Statistic (Computed) 1.99 -2.51 Group 2 105 40 5 Lower Crit Value Upper Crit Value p -Value Two-Tailed Test H1: (m1 m2) -1.9600 1.9600 0.0143 Upper-Tail Test H1: (m1 > m2 OR m2 < m1) n/a 1.6449 0.9929 Lower-Tail Test H1: (m1 < m2 OR m2 > m1) -1.6449 n/a 0.0071 If you REJECT the null hypothesis, conclude that H1 is true. If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true. NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null). ©2007 DrJimMirabella.com dent Samples) Decision Reject the null hypothesis Do not reject the null hypothesis Reject the null hypothesis at H1 is true. ence to conclude that H1 is true. NNOT ACCEPT the null). Two Sample Hypothesis Test for the Mean (Independent Samples) Group 1 Group 2 2 4 9 3 2 3 7 5 8 4 3 Level of Significance 0.05 Sample Mean Sample Size Sample Standard Deviation Group 1 4.000 5 2.915 Standard Error (Computed) Test Statistic (Computed) 1.51 -0.66 Group 2 5.000 6 2.098 Lower Crit Value Upper Crit Value p -Value Two-Tailed Test H1: (m1 m2) -2.2622 2.2622 0.5245 Upper-Tail Test H1: (m1 > m2 OR m2 < m1) n/a 1.8331 0.7392 Lower-Tail Test H1: (m1 < m2 OR m2 > m1) -1.8331 n/a 0.2608 If you REJECT the null hypothesis, conclude that H1 is true. If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude th NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the ©2007 DrJimMirabella.com nt Samples) Decision Do not reject the null hypothesis Do not reject the null hypothesis Do not reject the null hypothesis conclude that H1 is true. ufficient evidence to conclude that H1 is true. e (i.e., we CANNOT ACCEPT the null). Two Sample Hypothesis Test for the Mean (Paired Samples) Item 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 Condition 1 Condition 2 135 110 131 142 105 130 131 110 125 149 128 105 119 140 98 123 127 115 122 145 Level of Significance 0.05 Standard Error (Computed) Test Statistic (Computed) 4.40 3.30 Lower Crit Value Two-Tailed Test H1: (md 0), (m1 m2) -2.2622 Upper-Tail Test H1: (md > 0), (m1 > m2 OR m2 < m1) n/a Lower-Tail Test H1: (md < 0), (m1 < m2 OR m2 > m1) -1.8331 If you REJECT the null hypothesis, conclu If you DO NOT REJECT the null hypothesis, there is insufficie NEVER conclude that the null hypothesis is true (i.e., ©2007 DrJimMirabella.com 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 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 Upper Crit Value p -Value Decision 2.2622 0.0092 Reject the null hypothesis 1.8331 0.0046 Reject the null hypothesis n/a 0.9954 Do not reject the null hypothesis T the null hypothesis, conclude that H1 is true. pothesis, there is insufficient evidence to conclude that H1 is true. null hypothesis is true (i.e., we CANNOT ACCEPT the null). ©2007 DrJimMirabella.com Two Sample Hypothesis Test for the Proportion Level of Significance 0.05 Number of Successes Sample Size Group 1 60 100 Group 2 140 200 Proportion (Computed) 0.60 0.70 Z Test Statistic (Computed) -1.73 Lower Crit Value Upper Crit Value p -Value Two-Tailed Test H1: (P1 P2) -1.9600 1.9600 0.0833 Upper-Tail Test H1: (P1 > P2 or P2 < P1) n/a 1.6449 0.9584 Lower-Tail Test H1: (P1 < P2 or P2 > P1) -1.6449 n/a 0.0416 If you REJECT the null hypothesis, conclude that H1 is true. If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true. NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null). ©2007 DrJimMirabella.com Decision Do not reject the null hypothesis Do not reject the null hypothesis Reject the null hypothesis at H1 is true. ence to conclude that H1 is true. NNOT ACCEPT the null). ANOVA Analysis of Variance Group A 18,5 24 17,2 19,9 18 17,99 17,48 16,97 16,46 15,95 15,44 14,93 14,42 13,91 13,4 12,89 12,38 11,87 11,36 10,85 10,34 9,83 17,2 19,9 18 Group B 26,3 25,3 24 21,2 24,5 21,95 21,18 20,41 19,64 18,87 18,1 17,33 16,56 15,79 15,02 14,25 13,48 12,71 11,94 11,17 Group C 20,6 25,2 20,8 24,7 22,9 24,07 24,48 24,89 25,3 25,71 26,12 26,53 26,94 27,35 27,76 Group D 25,4 19,9 22,6 17,5 20,4 17,44 16,2 14,96 13,72 12,48 Group E 12,48 14,96 17,44 17,5 19,9 SUMMARY Groups Group A Group B Group C Group D Group E ANOVA Source of Variation Treatment Error Total Null hypothesis: Alternate hypothesis: Significance level: p-Value Decision: Count 25 20 15 10 5 Sum 389,170 369,700 373,350 180,600 82,280 Average 15,567 18,485 24,890 18,060 16,456 Variance 11,968 21,215 4,543 16,343 7,991 SS 849,633 932,971 df 4 70 MS 212,408 13,328 F 15,937 1782,604 74 287,2369 403,0815 63,599 147,088 31,96592 3,650776 F crit 2,503 m1 = m2 = m3 = m4 = m5 Not all the means are equal 0,05 0,0000 Reject the null hypothesis Mean Differences Post-Hoc Tests Difference Comparison of Means Group A to Group B 2,918 Group A to Group C 9,323 Group B to Group C 6,405 Group A to Group D 2,493 Group B to Group D 0,425 Group C to Group D 6,830 Group A to Group E 0,889 Group B to Group E 2,029 Group C to Group E 8,434 Group D to Group E 1,604 Lower Conf. Limit 0,734 6,945 3,918 -0,231 -2,395 3,857 -2,678 -1,612 4,674 -2,384 Upper Conf. Limit 5,103 11,701 8,892 5,218 3,245 9,803 4,456 5,670 12,194 5,592 ©2007 DrJimMirabella.com Difference in Treatment Means??? ***Means are different*** ***Means are different*** ***Means are different*** - no difference - no difference ***Means are different*** - no difference - no difference ***Means are different*** - no difference - Group A Group B Group C Group D Group E 17,023 20,113 26,770 20,363 17,626 14,111 16,857 23,010 15,757 15,286 15,567 18,485 24,890 18,060 16,456 Confidence Intervals of Groups 30 26,770 25 23,010 20,363 20,113 20 17,023 17,626 16,857 15,757 15 15,286 14,111 10 5 0 Group A Group B Group C Group D Group E Sample Size Determination for Proportion Estimate of True Proportion* = Sampling Error = Confidence Level = Finite Population Size = 0.50 0.05 95.00% Sample Size Needed = 385 500 Sample Size Needed = 218 *Use .50 for the "estimate of true proportion" when unknown. Sample Size Determination for Mean Population Standard Deviation = Sampling Error = Confidence Level = Finite Population Size = 100 25 95.00% Sample Size Needed = 62 500 Sample Size Needed = 55 ©2007 DrJimMirabella.com
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