2. An experiment was conducted to compare the mean absorption of two drugs in muscle tissue. Muscle tissue specimens were randomly divided into two groups of equal size. Group 1 was tested with Drug 1 and Group 2 was tested with Drug 2. Assuming that the absorption rate is approximately normally distributed for each drug with equal population standard deviation, a 99% condence estimate for the difference in population means (Group 1 mean minus Group 2 mean) is (-0.1067, 0.5407). (a) Explain why the sample standard deviations should be pooled in this situation. (b) Explain why this condence interval does not provide statistical evidence that there is a difference in mean absorption. (c) How could the interval potentially be changed to provide statistical evidence of a difference? 3. In a study to investigate the effect of diet on reducing cholesterol levels, a random sample of 12 subjects known to have high cholesterol had their cholesterol measured at he beginning of the study and again after six months on a special diet. Suppose that you could assume that the differences in cholesterol (before minus after) are a random sample from some approximately normal population. (a) What test would you use to asses if the special diet is effective at reducing cholesterol levels? State clearly the appropriate hypothesis. (b) Suppose that the mean difference (before minus after) is 8 and the standard error of the mean difference is 4.88. Compute and report the corresponding p-value and give your decision at a 5% level of signicance. (c) An important assumption in performing the above test was that the distributions of the differences is approximately normal. Explain how you should assess the validity of this assumption