A study has been made to compare the nicotine contents of two brands of cigarettes. Ten cigarettes of Brand A had an average nicotine content of 4 milligrams with a standard deviation of 0.5 milligram. Eight cigarettes of Brand B had an average nicotine content of 2.9 milligrams with a standard deviation of 0.5 milligram. Assume that the two sets of data are independent random samples from normal populations with equal variances. Answer the following, and round off your answer to three decimal places. (a) Find a pooled estimate of the population standard deviation (b) With 95% confidence, what is the largest amount by which the nicotin content of Brand A exceeds that of Brand B