Continuation of Problem 2.42. Suppose that we want to construct a 95% two-sided confidence interval on the difference in two means where the two sample standard deviations are known to be ????1 = 4 and ????2 = 8. The total sample size is restricted to N = 30. What is the length of the 95% CI if the sample sizes used by the experimenter are n1 = n2 = 15? How much shorter would the 95% CI have been if the experimenter had used an optimal sample size allocation?