Data Driven Statistics

May 10th, 2013
SoccerBoss
Category:
Other
Price: $15 USD

Question description

Parts I–II: Review and revise your individual project from last week. You must include parts I and II from Individual Project #4 as they will be graded again. Then, add the following responses to your document:

Part III: Regression and Correlation

Based on what you have learned from your research on regression analysis and correlation, answer the following questions about the Body Fat Versus Weight data set:

  • When performing a regression analysis, it is important to first identify your independent/predictor variable versus your dependent/response variable, or simply put, your x versus y variables. How do you decide which variable is your predictor variable and which is your response variable? 
  • Based on the Body Fat Versus Weight data set, which variable is the predictor variable? Which variable is the response variable? Explain.
  • Using Excel, construct a scatter plot of your data.
  • Using the graph and intuition, determine whether there is a positive correlation, a negative correlation, or no correlation. How did you come to this conclusion?
  • Calculate the correlation coefficient, r, and verify your conclusion with your scatter plot. What does the correlation coefficient determine? Discuss the strength of the correlation coefficient calculated, and if the correlation is positive or negative.
  • Add a regression line to your scatter plot, and obtain the regression equation.
    • Does the line appear to be a good fit for the data? Why or why not?
    • Regression equations help you make predictions. Using your regression equation, discuss what the slope means, and determine the predicted value of body fat x = 0. Interpret the meaning of this equation.

Part IV: Putting it Together

Your analysis is now complete, and you are ready to report your findings to your boss. In one paragraph, summarize your results by explaining your findings from the statistical measures, hypothesis test, and regression analysis of body fat and weight for the 252 men attending Silver’s Gym


INFO That MAY NEEDED

Part I

The mean, median, range, and standard deviation for the Body Fat and Weight data are computed in the following Table

Measure

BODYFAT

WEIGHT

Mean

18.94

178.92

Median

19.00

176.50

Range

45.10

244.65

Standard Deviation

7.75

29.39

Mean and median are two commonly used measures of central tendency.  Mean is the sum of observa­tions divided by the total number of observations. Median is the midpoint of the values after all observations have been ordered from the smallest to the largest. The average body fat and weight of men who attend the gym are 18.94 and 178.92 respectively. The median values of body fat and weight are 19.0 and 176.5 respectively. The mean and median values of body fat and weight are close. Range and Standard deviation are measures of dispersion. They show the variability in the data. Range is the difference between the largest and smallest values in a data set. Standard deviation is the square root of the arithmetic mean of the squared deviations from the mean.

The purpose of mean and median is to pinpoint the center of a set of observations. Mean and median are useful measure for comparing two or more populations.

The mean is not representative of data with extreme values. The median is a useful measure when we encounter data with an extreme value. In this data set, the mean may be more useful than the median, because of the relatively large sample size which will not be as heavily impacted by statistical outliers.

A direct comparison of two sets of data based only on two measures of location such as the mean and the median can be misleading since an average does not tell us anything about the spread of the data. In such situation we use the measures of dispersion range or standard deviation.

Part II

Let μ denote the mean body fat in men attending Silver’s Gym.

The null and alternative hypotheses are

Ho: μ = 20

Ha: μ ≠ 20

Since the alternative hypothesis contains the not-equal-to symbol, the test is two-tailed test.

The significance level of the test is given to be α = 0.05.

Since the sample size (n = 252 > 30) is large, we can use the z–test for testing the hypothesis.

The critical values at α = 0.05 are –z0 = -1.96 and z0 = 1.96. Therefore, the rejection regions are to the left of –z0 = -1.96 and to the right of z0 = 1.96.

The standardized test statistic is

  z = (xbar – μ)/(σ/√n)

Since the sample size n > 30, we can use σ ≈ s, the sample standard deviation.

For the body fat data, n = 252, xbar = 18.94 and s = 7.75.

Therefore, z = (18.94 – 20)/(7.75/√252) = - 2.17

The decision rule is: Reject Ho if z < -1.96 or z > 1.96.

Since z < -1.96 it is in the rejection region and we reject the null hypothesis Ho.

Thus, there is sufficient evidence to reject the claim that the mean body fat in men attending Silver’s Gym is 20%.

Supplement:
IDNO BODYFAT WEIGHT
1 12.6 154.25 Description: The dataset provided here is based on a sample of 252 men.  
2 6.9 173.25 Their body fat and weights were recorded.  
3 24.6 154.00  
4 10.9 184.75 Statement: The doctors office claims that the mean body fat in men is 20%.  
5 27.8 184.25  
6 20.6 210.25 Source: http://www2.stetson.edu/~jrasp/data.htm  
7 19.0 181.00  
8 12.8 176.00  
9 5.1 191.00  
10 12.0 198.25  
11 7.5 186.25  
12 8.5 216.00  
13 20.5 180.50  
14 20.8 205.25  
15 21.7 187.75  
16 20.5 162.75                    
17 28.1 195.75                    
18 22.4 209.25                    
19 16.1 183.75                    
20 16.5 211.75                    
21 19.0 179.00                    
22 15.3 200.50                    
23 15.7 140.25                    
24 17.6 148.75                    
25 14.2 151.25                    
26 4.6 159.25                    
27 8.5 131.50                    
28 22.4 148.00                    
29 4.7 133.25                    
30 9.4 160.75                    
31 12.3 182.00                    
32 6.5 160.25                    
33 13.4 168.00                    
34 20.9 218.50                    
35 31.1 247.25                    
36 38.2 191.75                    
37 23.6 202.25                    
38 27.5 196.75                    
39 33.8 363.15                    
40 31.3 203.00                    
41 33.1 262.75                    
42 31.7 205.00                    
43 30.4 217.00                    
44 30.8 212.00                    
45 8.4 125.25                    
46 14.1 164.25                    
47 11.2 133.50                    
48 6.4 148.50                    
49 13.4 135.75                    
50 5.0 127.50                    
51 10.7 158.25                    
52 7.4 139.25                    
53 8.7 137.25                    
54 7.1 152.75                    
55 4.9 136.25                    
56 22.2 198.00                    
57 20.1 181.50                    
58 27.1 201.25                    
59 30.4 202.50                    
60 24.0 179.75                    
61 25.4 216.00                    
62 28.8 178.75                    
63 29.6 193.25                    
64 25.1 178.00                    
65 31.0 205.50                    
66 28.9 183.50                    
67 21.1 151.50                    
68 14.0 154.75                    
69 7.1 155.25                    
70 13.2 156.75                    
71 23.7 167.50                    
72 9.4 146.75                    
73 9.1 160.75                    
74 13.7 125.00                    
75 12.0 143.00                    
76 18.3 148.25                    
77 9.2 162.50                    
78 21.7 177.75                    
79 21.1 161.25                    
80 18.6 171.25                    
81 30.2 163.75                    
82 26.0 150.25                    
83 18.2 190.25                    
84 26.2 170.75                    
85 26.1 168.00                    
86 25.8 167.00                    
87 15.0 157.75                    
88 22.6 160.00                    
89 8.8 176.75                    
90 14.3 176.00                    
91 20.2 177.00                    
92 18.1 179.75                    
93 9.2 165.25                    
94 24.2 192.50                    
95 9.6 184.25                    
96 17.3 224.50                    
97 10.1 188.75                    
98 11.1 162.50                    
99 17.7 156.50                    
100 21.7 197.00                    
101 20.8 198.50                    
102 20.1 173.75                    
103 19.8 172.75                    
104 21.9 196.75                    
105 24.7 177.00                    
106 17.8 165.50                    
107 19.1 200.25                    
108 18.2 203.25                    
109 17.2 194.00                    
110 21.0 168.50                    
111 19.5 170.75                    
112 27.1 183.25                    
113 21.6 178.25                    
114 20.9 163.00                    
115 25.9 175.25                    
116 16.7 158.00                    
117 19.8 177.25                    
118 14.1 179.00                    
119 25.1 191.00                    
120 17.9 187.50                    
121 27.0 206.50                    
122 24.6 185.25                    
123 14.8 160.25                    
124 16.0 151.50                    
125 14.0 161.00                    
126 17.4 167.00                    
127 26.4 177.50                    
128 17.4 152.25                    
129 20.4 192.25                    
130 15.0 165.25                    
131 18.0 171.75                    
132 22.2 171.25                    
133 23.1 197.00                    
134 25.3 157.00                    
135 23.8 168.25                    
136 26.3 186.00                    
137 21.4 166.75                    
138 28.4 187.75                    
139 21.8 168.25                    
140 20.1 212.75                    
141 24.3 176.75                    
142 18.1 173.25                    
143 22.7 167.00                    
144 9.9 159.75                    
145 10.8 188.15                    
146 14.4 156.00                    
147 19.0 208.50                    
148 28.6 206.50                    
149 6.1 143.75                    
150 24.5 223.00                    
151 9.9 152.25                    
152 19.1 241.75                    
153 10.6 146.00                    
154 16.5 156.75                    
155 20.5 200.25                    
156 17.2 171.50                    
157 30.1 205.75                    
158 10.5 182.50                    
159 12.8 136.50                    
160 22.0 177.25                    
161 9.9 151.25                    
162 14.8 196.00                    
163 13.3 184.25                    
164 15.2 140.00                    
165 26.5 218.75                    
166 19.0 217.00                    
167 21.4 166.25                    
168 20.0 224.75                    
169 34.7 228.25                    
170 16.5 172.75                    
171 4.1 152.25                    
172 1.9 125.75                    
173 20.2 177.25                    
174 16.8 176.25                    
175 24.6 226.75                    
176 10.4 145.25                    
177 13.4 151.00                    
178 28.8 241.25                    
179 22.0 187.25                    
180 16.8 234.75                    
181 25.8 219.25                    
182 0.0 118.50                    
183 11.9 145.75                    
184 12.4 159.25                    
185 17.4 170.50                    
186 9.2 167.50                    
187 23.0 232.75                    
188 20.1 210.50                    
189 20.2 202.25                    
190 23.8 185.00                    
191 11.8 153.00                    
192 36.5 244.25                    
193 16.0 193.50                    
194 24.0 224.75                    
195 22.3 162.75                    
196 24.8 180.00                    
197 21.5 156.25                    
198 17.6 168.00                    
199 7.3 167.25                    
200 22.6 170.75                    
201 12.5 178.25                    
202 21.7 150.00                    
203 27.7 200.50                    
204 6.8 184.00                    
205 33.4 223.00                    
206 16.6 208.75                    
207 31.7 166.00                    
208 31.5 195.00                    
209 10.1 160.50                    
210 11.3 159.75                    
211 7.8 140.50                    
212 26.4 216.25                    
213 19.3 168.25                    
214 18.5 194.75                    
215 19.3 172.75                    
216 45.1 219.00                    
217 13.8 149.25                    
218 8.2 154.50                    
219 23.9 199.25                    
220 15.1 154.50                    
221 12.7 153.25                    
222 25.3 230.00                    
223 11.9 161.75                    
224 6.1 142.25                    
225 11.3 179.75                    
226 12.8 126.50                    
227 14.9 169.50                    
228 24.5 198.50                    
229 15.0 174.50                    
230 16.9 167.75                    
231 11.1 147.75                    
232 16.1 182.25                    
233 15.5 175.50                    
234 25.9 161.75                    
235 25.5 157.75                    
236 18.4 168.75                    
237 24.0 191.50                    
238 26.4 219.15                    
239 12.7 155.25                    
240 28.8 189.75                    
241 17.0 127.50                    
242 33.6 224.50                    
243 29.3 234.25                    
244 31.4 227.75                    
245 28.1 199.50                    
246 15.3 155.50                    
247 29.1 215.50                    
248 11.5 134.25                    
249 32.3 201.00                    
250 28.3 186.75                    
251 25.3 190.75                    
252 30.7 207.50                    

mongo0517 days ago


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