A company claims that its medicine, Brand A, gives faster relief from pain than another company's medicine, Brand B. A researcher tested both brands of medicine on two groups of randomly chosen patients. The results of 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 25 44 11
B 22 49 9
Test at the 1% significance level whether mean relief time for Brand A is less than that for Brand B. Suppose that the two populations are normally distributed and population variances are unknown