Question: Problem 4. [6 pts] Suppose X1, . . ., Xn are i.i.d. N(ux, ox ) and Y1, ..., Ym are i.i.d. N(MY, of). and Xi's

Problem 4. [6 pts] Suppose X1, . . ., Xn are i.i.d. N(ux, ox ) and Y1, ..., Ym are i.i.d. N(MY, of). and Xi's are independent of Yi's. If ux and my are known, we then estimate of and of by their MLEs respectively n m E(Xi -ux)? and n [( vi - MY)? m i=1 i=1 Design a test statistic based on of and of to test Ho : 0x = of against H1 : ox > o. Derive the distribution under Ho for the test statistic you would use and work out the critical region given the significance level a

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