A class has 2n a large number students the students are

Question

A class has 2n (a large number) students The students are separated into two groups A and B each with n students. Group A students take exam A and earn iid scores X₁,..., X_n. Group B students take exam B, earning iid scores Y₁,..., Y_n. The two exams are similar but different; however, the exams were designed so that a student's score X on exam A or Y on exam B have the same mean and variance σ² = 100. For each exam, we form the sample mean statistic

Based on the statistic D = MA - MB, use the central limit theorem to design a significance test at significance level α = 0.05 for the hypothesis H₀ that a students score on the two exams has the same mean µ and variance σ² = 100. What is the rejection region if n = 100? Make sure to specify any additional assumptions that you need to make; however, try to make as few additional assumptions as possible