Question

Height

162.5

175.5

160

175

158

163

186

165

155

165

172

168

175.5

158

188.5

162.5

183

162.5

180.5

171

180.5

180.5

176

175

173

165.5

160

161.5

174

165

178

164

153

183

162.5

178

178

168.5

162.5

185.5

176.5

188

167

155

160.5

173

177.5

180

178

171.5

168

164.5

170.5

168

160.5

165

157

161.5

157.5

173

Lastly, although the procedure in #3 above was convenient, in most cases if we are trying to predict the population mean from a sample mean, we will most likely not know the population standard deviation, sigma. Thus, our next best statistic to use is the sample standard deviation in its place. However, when using the sample standard deviation, we are no longer able to use a normal distribution, and must use the t-distribution instead. a. Determine the margin of error in estimating the population mean height from this one sample’s mean based upon a 95% level of confidence. Do NOT USE our earlier assumption of sigma = 10.2 cm, but use the sample standard deviation value you calculated in 3a, along with appropriate t-score instead of a z-score. b. Using your margin of error value from (5a), give the 95% confidence interval for the population mean height measure as predicted from this one sample's results. State this interval below within an interpretive sentence.

Answer 1

Solution:-

a)

Mean = 169.7167

Median = 168.25

Mode = 162.5

Variance = 82.96921

Height
Mean	169.7167
Standard Error	1.175934
Median	168.25
Mode	162.5
Standard Deviation	9.108744
Sample Variance	82.96921
Kurtosis	-0.88965
Skewness	0.209291
Range	35.5
Minimum	153
Maximum	188.5
Sum	10183
Count	60

b)

M.E = 2.353

c) 95% confidence interval for the mean is C.I = ( 167.364, 172.069).

C.I = 169.7167 + 2.353

C.I = ( 167.364, 172.069)

If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals (167.364, 172.069) would contain the population mean.