1. The problem statement, all variables and given/known data A study of weight gain in male rats compared two diets, A and B, which were formulated in terms of level and source of protein. A total of twenty two rats were randomly assigned to the diets, eleven to each diet. Summary statistics for the weight gains (grams) by the end of the study are shown. A B Mean 99.5 78.7 St. Dev 10.9 16.5 n 11 11 (a) An F-test was carried out to compare the sample standard deviations. Why might this have been done? Carry out the F-test: specify the null hypothesis, the significance level and critical value you use in the test and intrepret the test result. (b) Carry out a t-test to compare the sample means. State ecplicitly the null hypothesis, the degrees of freedom for the reference distribution, and the critical values for your test. Interpret the results of the test in practical terms. (c) It has been suggested that rather than carry out a test, it would be better to calculate a confidence interval. Explain why this is either correct or not correct. Calculate and interpret an appropriate confidence interval. (d) It was asserted that had the raw data been available, a paired t-test would be the appropriate test for analyzing the study results. Discuss. (e) Before a study such as this one can be carried out, the researchers need to decide on a sample size for the study. Discuss the issues that need to be considered in arriving at a suitable sample size for this type of study. 2. Relevant equations 3. The attempt at a solution (a) I used F = (s1)^2/(s2)^2 This gave (16.5)^2/(10.9)^2 = 2.29 The null hypotheses, Ho: s1=s2 Is this correct? I don't know how to get the significance level or critical value. (b) I used t = (x1 - x2)/root[(s1^2 - s2^2)/n) which gave me 3.49 Ho: u1 = u2 11-1=10 degrees of freedom Is it okay to do a 95% confidence interval? That's what all the examples do, but I don't know why... (c) Using (x1 - x2)+-t*(root[(s1^2 - s2^2)/n) I need to get t* from the previous part. For (d) and (e) any advice would be greatly appreciated as I'm lost.