Analysis of Scientific Data - Summer 2020 Week 4 Tutorial Part A - Paired T Test 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 4 5 6 7 8 9 Drug A 74 55 61 47 53 74 52 40 50 Drug B 63 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. H0: H1: b) Calculate the tstatistic 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? Part B A sample of 9 speedometers of a particular brand was obtained and each was calibrated to check for accuracy at 100 km/h. The resulting average and sample deviation arex# 98.5 km/h and s = 2.2 km/h, respectively. Let u denote the true average reading when the actual speed is 100 kmh. (a) Construct a 95% confidence interval foru. (b) Does the sample evidence suggest that u # 100 km/h at the 5% level? (c) What is the P -value for this test? (d) If 2.2 were able to be taken to be the population standard deviation rather than the sample estimate, would the outcome of the test still be the same at the 5% level? You may find the following output from R useful in answering the questions on this sheet. > pt(0.7454,df=8) [1] 0.7613218 > 1-pt(2.2362,df=8) [1] 0.02787752 > pt(2.2362,df=9) [1] 0.973917 > pt(2.2362,df=8) [1] 0.9721225 >qt(.95,df=8) [1] 1.859548 > qt(.975,df=8) [1] 2.306004 >2*pt(2.045455, df=8) [1] 0.07503578 >2*pnorm(2.04545 5) [1] 0.04081002