Question

# Height 162.5 175.5 160 175 158 163 186 165 155 165 172 168 175.5 158 188.5...

 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.

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.