The National Health Statistics Reports dates Oct. 22, 2008 included the following information on the heights in inches for non-Hispanic white females.
Age Sample Size Sample Mean Standard Error Mean
20-39 866 64.9 0.09
60+ 934 63.1 0.11
a. Calculate and interpret a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women.
b. Let ? denote the population mean height for those aged 20-39 and ? denote the population mean height for those ages 60 and older. Interpret the hypotheses ?, and then carry out a test of these hypotheses at significance level 0.001 using the rejection region approach.
c. What is the P-value for the test you carried out in (b)? Based on this P-value, would you reject the null hypothesis at any reasonable level of significance?
d. What hypotheses would be appropriate if ?referred to the older age group and ?referred to the younger age group and you wanted to see if there was compelling evidence for concluding that the population mean height for younger women exceeded that for older women by more than one inch?