Question: A company claims that its medicine, Brand A, provides faster relief from pain than another company's medicine, Brand B. A researcher tested both brands of medicine on two groups of randomly selected patients. The results of the test are given in the following table. The mean and standard deviation of relief times are in minutes.

Brand           Sample Size         Mean of Relief Times          Standard Deviation of Relief Times

A                     22                            44                                        11

B                     22                            49                                         9

a. Construct a 99% confidence interval for the difference between the mean relief times for the two brands of medicine.

b. Test at the 1% significance level whether the mean relief time for Brand A is less than that for Brand B. Assume that the two populations are normally distributed with unknown but equal standard deviations.