Trials are carried out on a new tablet to help ease joint pain for people with chronic arthritis. A randomly selected sample of eight patients who have been suffering from arthritis are given the new tablets. Each participant measures the time it takes for the pain to stop after taking a new tablet as soon as they wake in the morning. The times, in minutes, are:

34,44,25,30,8,27,41,31

The average waiting time for the old type of tablet is 43 minutes after awakening.

a. Carry nut a Wilcoxon signed-rank test, at the 5% significance level, to investigate whether the new tablets offer faster pain relief.

b. Give a reason why the Wilcoxon signed-rank test might be preferred to a sign test.