In the following problem we discuss the test comparing two distribution means with the same variance. Assume X m N{m , 0'2). Y m N (#2, 0'2), and they are independent. . What is the variance of X Y? 202 O 02/2 . If E is the sample mean of n independent random observations of X and i} is the sample mean of n independent random observations of Y, what distribution does X Y follow? 0 Ma was) 0 Ma -#21%) O Nip-1 -u2, 2\"! 11. . We now want to test the null hypothesis H0 H0 : In college, the average GPA of men is equal to the average GPA of women. H1 : In college, the average GPA of men is different from the average GPA of women. A sample of 'IO men's GPA in college has sample mean 2.9, and a sample of 10 women's GPA has sample mean 3.1. We also know the GPAs of men and women have the same standard deviation 0.2. Calculate the p value. The checker accepts answers with tolerance E1001