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2. A study has been made to compare the nicotine contents of two types 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. (a) Find a 93%, two-sided symmetric confidence interval for the difference between the mean nicotine contents Of two brands Of cigarettes. Notice that because this confidence interval is symmetric, it means that lower 2.5% Of the points are outside this confidence interval and so are the upper 2.5% of the points. (b) Find a 95% two-sided asymmetric confidence interval such that lower of points are outside the confidence interval and upper of the points are outside that confidence interval. Note that - 2.5835, - 1.8693, toxn(18) 2.5524, 1.8553. (c) Find the length of the two constructed confidence intervals and state which confidence inter- vals is narrower. (d) Which of the two confidence intervals do you prefer and why?