Resting heart rate was compared for a random sample of healthy adult men and women of the same age. The 15 women sampled had a resting heart rate of 78 beats per minute with standard deviation 5 bpm. The resting heart rate for the sampled 18 men was 71 bpm with standard deviation 3 bpm.

a) Should the results best be analysed as paired data or two independent means? Explain.

b) Do women of this age have a significantly higher resting heart rate than men? Carry out a hypothesis test with a significance level of 5%, including all steps.

c) Create a 90% confidence interval for the mean difference in heart rate, and interpret the interval in context.

d) Is the confidence interval consistent with your hypothesis test conclusion? Explain.

e) Is it necessary for the test you used that resting heart rate is normally distributed? Explain.