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You are hired as a...

You are hired as a statistical analyst for Silver’s Gym, and your boss wants to examine the relationship between body fat and weight in men who attend the gym. After compiling the data for weight and body fat of 252 men who attend Silver’s Gym, you find it relevant to examine the statistical measures and to perform hypothesis tests and regression analysis to help make general conclusions for body fat and weight in men.

Part I: Statistical Measures

Statistics is a very powerful topic that is used on a daily basis in many situations. For example, you may be interested in the age of the men who attend Silver’s Gym. You could not assume that all men are the same age. Thus, it would be an inaccurate measure to state that "the average age of men who attend Silver’s Gym is the same age as me."

Averages are only one type of statistical measurements that may be of interest. For example, your company likes to gauge sales during a certain time of year and to keep costs low to a point that the business is making money. These various statistical measurements are important in the world of statistics because they help you make general conclusions about a given population or sample.

To assist in your analysis for Silver’s Gym, answer the following questions about the Body Fat Versus Weight data set:

Click here to download the Body Fat Weight data set.

IDNO BODYFAT WEIGHT

1 12.6 154.25

2 6.9 173.25

3 24.6 154.00

4 10.9 184.75

5 27.8 184.25

6 20.6 210.25

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

Calculate the mean, median, range, and standard deviation for the Body Fat Versus Weight data set. Report your findings, and interpret the meanings of each measurement.

The measures of central tendency are important in real-world situations.

What is the importance of finding the mean/median? Why might you find this information useful?

In some data sets, the mean is more important than the median. For example, you want to know your mean overall grade average because the median grade average would be meaningless. However, you might be interested in a median salary to see the middle value of where salaries fall. Explain which measure, the mean or the median, is more applicable for this data set.

What is the importance of finding the range/standard deviation? Why might you find this information useful?

Part II: Hypothesis Testing

Organizations sometimes want to go beyond describing the data and actually perform some type of inference on the data. Hypothesis testing is a statistical technique that is used to help make inferences about a population parameter. Hypothesis testing allows you to test whether a claim about a parameter is accurate or not.

Your boss makes the claim that the average body fat in men attending Silver’s Gym is 20%. You believe that the average body fat for men attending Silver’s Gym is not 20%. For claims such as this, you can set up a hypothesis test to reach one of two possible conclusions: either a decision cannot be made to disprove the body fat average of 20%, or there is enough evidence to say that the body fat average claim is inaccurate.

To assist in your analysis for Silver’s Gym, answer the following questions based on your boss’s claim that the mean body fat in men attending Silver’s Gym is 20%:

First, construct the null and alternative hypothesis test based on the claim by your boss.

Using an alpha level of 0.05, perform a hypothesis test, and report your findings. Be sure to discuss which test you will be using and the reason for selection.

Based on your results, interpret the final decision to report to your boss.

Parts I–II: Review and revise your individual project from last week. 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?

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 (y) when weight (x) equals 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.

Parts I–II: Review and revise your individual project from last week. 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?

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 (y) when weight (x) equals 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.

Part I: Statistical Measures

Statistics is a very powerful topic that is used on a daily basis in many situations. For example, you may be interested in the age of the men who attend Silver’s Gym. You could not assume that all men are the same age. Thus, it would be an inaccurate measure to state that "the average age of men who attend Silver’s Gym is the same age as me."

Averages are only one type of statistical measurements that may be of interest. For example, your company likes to gauge sales during a certain time of year and to keep costs low to a point that the business is making money. These various statistical measurements are important in the world of statistics because they help you make general conclusions about a given population or sample.

To assist in your analysis for Silver’s Gym, answer the following questions about the Body Fat Versus Weight data set:

Click here to download the Body Fat Weight data set.

IDNO BODYFAT WEIGHT

1 12.6 154.25

2 6.9 173.25

3 24.6 154.00

4 10.9 184.75

5 27.8 184.25

6 20.6 210.25

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

Calculate the mean, median, range, and standard deviation for the Body Fat Versus Weight data set. Report your findings, and interpret the meanings of each measurement.

The measures of central tendency are important in real-world situations.

What is the importance of finding the mean/median? Why might you find this information useful?

In some data sets, the mean is more important than the median. For example, you want to know your mean overall grade average because the median grade average would be meaningless. However, you might be interested in a median salary to see the middle value of where salaries fall. Explain which measure, the mean or the median, is more applicable for this data set.

What is the importance of finding the range/standard deviation? Why might you find this information useful?

Part II: Hypothesis Testing

Organizations sometimes want to go beyond describing the data and actually perform some type of inference on the data. Hypothesis testing is a statistical technique that is used to help make inferences about a population parameter. Hypothesis testing allows you to test whether a claim about a parameter is accurate or not.

Your boss makes the claim that the average body fat in men attending Silver’s Gym is 20%. You believe that the average body fat for men attending Silver’s Gym is not 20%. For claims such as this, you can set up a hypothesis test to reach one of two possible conclusions: either a decision cannot be made to disprove the body fat average of 20%, or there is enough evidence to say that the body fat average claim is inaccurate.

To assist in your analysis for Silver’s Gym, answer the following questions based on your boss’s claim that the mean body fat in men attending Silver’s Gym is 20%:

First, construct the null and alternative hypothesis test based on the claim by your boss.

Using an alpha level of 0.05, perform a hypothesis test, and report your findings. Be sure to discuss which test you will be using and the reason for selection.

Based on your results, interpret the final decision to report to your boss.

Parts I–II: Review and revise your individual project from last week. 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?

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 (y) when weight (x) equals 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.

Parts I–II: Review and revise your individual project from last week. 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?

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 (y) when weight (x) equals 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.

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IDNO BODYFAT WEIGHT 1 12.6 154.25 2 6.9 173.25 3 24.6 154.00 4 10.9 184.75 5 27.8 184

IDNO BODYFAT WEIGHT 1 12.6 154.25 2 6.9 173.25 3 24.6 154.00 4 10.9 184.75 5 27.8 184.25 6 20.6 210.25 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 20.5 180.5… read more

Part I: Statistical Measures Statistics is a very powerful

Part I: Statistical Measures Statistics is a very powerful topic that is used on a daily basis in many situations. For example, you may be interested in the age of the men who attend Silver's Gym. You… read more

Here it is Ryan, hope you can help, its Part 3 and 4 of the

Here it is Ryan, hope you can help, its Part 3 and 4 of the one you just helped me with. Part III: Regression and Correlation Based on what you have learned from your research on regression analysis a… read more

When perfoming a regression analysis,it is important to first

When perfoming a regression analysis,it is important to first identify your independent/predicto variable versus your dependent/respons variable,or simply put,your x versus y variables.How do you deci… read more

You are hired as a statistical analyst for Silvers Gym, and

You are hired as a statistical analyst for Silver's Gym, and your boss wants to examine the relationship between body fat and weight in men who attend the gym. After compiling the data for weight and … read more

For Susan Athena: Part III: Regression and Correlation Based

For Susan Athena: 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 Versu… read more

Part I: Statistical Measures Statistics is a very powerful

Attachment: 2012-02-07_021510_bodyfat_weight_data1.xls Part I: Statistical Measures Statistics is a very powerful topic that is used on a daily basis in many situations. For example, you may be intere… read more

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