Question

The BodyFat.xls data set contains measurements taken from 101 US men, collected in 2013. Use this data set to answer problems 3-4.

3) Find a 99% confidence interval for the mean weight of US men.

4) In 1960 the average weight of US men was 166 pounds. Does this data provide evidence at the α = 0.01 level that the average weight of US men has increased since then?

BodyFat.xls data

WEIGHT

154.25

173.25

154.00

184.75

184.25

210.25

181.00

176.00

191.00

198.25

186.25

216.00

180.50

205.25

187.75

162.75

195.75

209.25

183.75

211.75

179.00

200.50

140.25

148.75

151.25

159.25

131.50

148.00

133.25

160.75

182.00

160.25

168.00

218.50

247.25

191.75

202.25

196.75

363.15

203.00

262.75

205.00

217.00

212.00

125.25

164.25

133.50

148.50

135.75

127.50

158.25

139.25

137.25

152.75

136.25

198.00

181.50

201.25

202.50

179.75

216.00

178.75

193.25

178.00

205.50

183.50

151.50

154.75

155.25

156.75

167.50

146.75

160.75

125.00

143.00

148.25

162.50

177.75

161.25

171.25

163.75

150.25

190.25

170.75

168.00

167.00

157.75

160.00

176.75

176.00

177.00

179.75

165.25

192.50

184.25

224.50

188.75

162.50

156.50

197.00

198.50

Answer 1

Calculation:

Mean:

Standard deviation = S =

Degress of Freedom = n-1 = 101-1 = 100

Critical value: for = 0.01

..............Using t table

99% Confidence interval:

4)

n = 101, = 177.17, S = 32.57, = 166, = 0.01

Hypothesis:

Ho: = 166

Ha: > 166

Test statistic:

P-value= 0.0004 ...........Using t table

Conclusion:

P-value < , i.e. 0.0004 < 0.01, That is Reject Ho at 1% level of significance.

Therefore, The data provide Sufficient evidence at the α = 0.01 level that the average weight of US men has increased since then.