Analysis of Scientific Data - Semester One, 2022 Week 6 Tutorial Questions Part A Alice recruited nine pairs of identical twins for a study of two cholesterol-reducing drugs, A and B, with the aim of showing that drug A gave higher reductions in cholesterol than drug B. One of the twins in each pair was given drug A and the other was given drug B, where the choice was made at random. The amount by which cholesterol was reduced in each subject (mg/dL) is given in the following table: Pair 1 2 3 5 6 7 8 9 Drug A 74 55 61 47 53 74 52 10 50 Drug B 3 58 49 41 50 69 59 31 44 Difference 11 -3 12 6 3 5 -7 9 6 The sample mean difference in cholesterol reduction between drug A and drug B was 4.67 mg/dL with a sample standard deviation of 6.265 mg/dL. a) State the null and alternative hypotheses of interest in terms of u, the mean difference in cholesterol reduction between drug A and drug B in twins in this population. b) Calculate the t statistic to test this null hypothesis. c) What is the corresponding p-value? What do you conclude? d) Based on this data, calculate a 95% confidence interval for the mean difference in cholesterol reduction between drug A and drug B. e) Suppose we wanted to carry out a new study that could estimate the mean difference in cholesterol reduction with a margin of error of 2 mg/dl. What sample size should the new study use if we keep the 95% confidence level? (Assume that population standard deviation, o , is 6.265)