A clinic tested two medicines on patients to find the relief time from pain. Brand A medicine was given to 22 patients, and it produced a mean relief time of 14 minutes with a standard deviation of 4...

Extracted text: A clinic tested two medicines on patients to find the relief time from pain. Brand A medicine was given to 22 patients, and it produced a mean relief time of 14 minutes with a standard deviation of 4 minutes. Brand B medicine was given to 25 patients, and it produced a mean relief time of 12 minutes with a standard deviation of 3 minutes. Assume that the relief times for both medicines for all patients have normal distributions with equal standard deviations. (a) Write a 95% confidence interval for the difference between the mean relief times for these two medicines. (b) Test at the 5% significance level if the mean relief times for two brands of medicines are different.