On page 390, we presented data obtained by researchers studying the effect of hormone replacement therapy (HRT) on cholesterol levels. The researchers randomly divided 59 elderly women (75 years old or older) into a group of 39 women who were given HRT and a group of 20 women who were given placebo. Two of the variables considered were high-density-lipoprotein (HDL) cholesterol level and low-density-lipoprotein (LDL) cholesterol level. The subjects were measured on these two variables at the beginning of the experiment and then 9 months later. The table on page 390 presents statistics for the changes in levels, in milligrams per deciliter (mg/dL), between the measurements at 9 months and baseline. Perform the following inferences for use of either HRT or placebo over a 9-month period by elderly women. Interpret all of your results.
a. At the 5% significance level, do the data provide sufficient evidence to conclude that HRT is effective in raising HDL cholesterol level. Use a paired t-test.
b. Find a 90% confidence interval for the mean increase in HDL cholesterol level by use of HRT. Use the paired t-interval procedure.
c. Repeat part (a) for placebo.
d. Repeat part (b) for placebo.
e. At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, HRT raises HDL cholesterol level more than placebo? Use a nonpooled t-test.
f. Find a 90% confidence interval for the difference between the mean increases of HDL cholesterol level by use of HRT and placebo.
g. Repeat parts (a)-(f) for decrease of LDL cholesterol level.