The National Health Statistics Reports dated Oct. 22, 2008, included the following infor...

The National Health Statistics Reports dated Oct. 22, 2008, included the following information on the heights (in.) for non-Hispanic white females:

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 μ₁ denote the population mean height for those aged 20–39 and μ2 denote the population mean height for those aged 60 and older. Interpret the hypotheses H₀: μ₁ – μ₂ = 1 and H_a: μ₁ – μ₂ > 1 and , and then carry out a test of these hypotheses at significance level .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 significance level? Explain.

d. What hypotheses would be appropriate if μ₁ referred to the older age group, μ₂ 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 1 in.?