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 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 µ, 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, 𝜎 , is 6.265)
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 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 µ, 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, 𝜎 , is 6.265)
