3. Estrogen is taken by millions of American women to treat symptoms of menopause or prevent osteoporosis. A study was conducted to assess if using estrogen therapy can lower the risk of dying from heart disease. Researchers randomly assigned 100 women (who were all under 75 years of age) to one of two groups. Group I received estrogen therapy, while Group II received an inert substitute. The study lasted 10 years and found that the women under 75 who had estrogen therapy for at least 10 years had a lower risk of dying from heart disease than those who had not received the estrogen. This result was statistically significant at the 5% level.

(a) Is it an experimental or observational study? Experimental study (b) What is the response variable? Response variable: Estrogen lowers the risk of dying from heart disease (c) What is the explanatory variable? How many levels does the explanatory variable have? Explanatory variable: 100 women under 75, 10 years, 5% significance level. So there was 3 levels. (d) It is stated that one group received an "inert substitute." What would this be in statistical terms? Null hypothesis. H:0 (e) State the null and alternative hypotheses regarding the populations being compared. H0: Women who take estrogen are not at a higher risk of dying from heart disease. H1: Women who take estrogen are at a lower risk of dying from heart disease. (f) What can you say about the p-value for this study? Be as specific as possible. (g) Could an error have been made? If yes, what type?