2.41. Continuation of Problem 2.40. 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?