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 milligrams with a standard deviation of milligram. Eight cigarettes of Brand B had an average nicotine content of milligrams with a standard deviation of 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) Construct a 95% confidence interval for the difference between the mean nicotine contents of the two brands of cigarettes. ( , )