Let X and Y denote the respective lengths of male and female green lynx spiders. Assume that the distributions of X and Y are N(μX, σ2x) and N(μY, σ2Y), respectively, and that σ2Y > σ2x. Thus, use the modification of Z to test the hypothesis H0: μX − μY = 0 against the alternative hypothesis H1: μX − μY < 0.
(a) Define the test statistic and a critical region that has a significance level of α = 0.025.
(b) Using the data given in Exercise 7.2-5, calculate the value of the test statistic and state your conclusion.
(c) Draw two box-and-whisker diagrams on the same figure. Does your figure confirm the conclusion of this exercise?