2. A study has been made to compare the nicotine contents of two types of cigarettes. Ten cigarettes of Brand A had an average nicotine content of 3.1 milligrams with a standard deviation of 0.5 milligrams, while eight cigarettes of Brand B had an average nicotine content of 2.7 milligrams with a standard deviation of 0.7 milligrams. Assume that the two sets of data are independent random samples from normal populations. If we also assume that the populations have equal variances, find a 95% confidence interval for the difference between the mean nicotine contents of the two brands of cigarettes. 3. Refer to problem 2. (a) Find a 99% confidence interval for the variance σ of the nicotine content of the Brand A cigarettes. (b) Find a 98% confidence interval for 02/14/0.