An issue of Science News (Vol. 163, No. 22, pp. 341–342) reported that the Women’s Health Initiative cast doubts on the benefit of hormonereplacement therapy. Researchers randomly divided 4532 healthy women over the age of 65 years into two groups. One group, consisting of 2229 women, received hormone-replacement therapy; the other group, consisting of 2303 women, received placebo. Over 5 years, 40 of the women receiving the hormonereplacement therapy were diagnosed with dementia, compared with 21 of those getting placebo.
a. At the 5% significance level, do the data provide sufficient evidence to conclude that healthy women over 65 years old who take hormone-replacement therapy are at greater risk for dementia than those who do not?
b. Determine and interpret a 95% confidence interval for the difference in dementia risk rates for healthy women over 65 years old who take hormone-replacement therapy and those who do not.