When you use R to perform any analyses to answer questions in the Exam, please providethe R output (statistical output or graphs) as a part of your answer. If not explicitly indicated in the problem, assume significance level (?) of 0.05

9. [Total: 18 pts] A study investigated the effect of different calcium supplementations on bone loss among postmenopausal women. Women volunteering for the study were randomized to one of three treatment groups: group 1 - estrogen cream and placebo calcium (n = 12); group 2 - placebo estrogen cream and 2000 mg/day of calcium (n = 12); group 3 - placebo estrogen cream and placebo calcium (n = 12). The rate of bone loss was calculated for each woman and expressed as a percent of initial bone mass. The mean and standard deviation are given below for each group. Group Mean rate of bone loss (%/year) Std.Dev. (%/year) 1 0.6 1.6 2 2.1 2.7 3 33 15 a) [2 pts] State the null hypothesis. Be as specific as possible such that whoever reads the null hypothesis will have complete information of what is being tested. b) [6 pts] State the statistical procedure you are using. Calculate the appropriate test statistic. Show all your calculations. Report the calculated values to 2 decimal places. c) [1 pts] Calculate the degrees of freedom used in the statistical test. d) [1 pts] What is the critical value of the test statistic for & = 0.05? You may use R to obtain this value. Report to 2 decimal places. Reject or accept the null hypothesis in a)? e) [4 pts] Use the Holm t test to compare all possible groups pairwise. Which pairs are different using an overall level of significance of 0.05. Fill in the table below. Show the formula(s) you used in answering this question. Pairwise comparisons using Holm t test Comparison t P (uncorrected) J* Pt (Or aj-) P