т 2 = d- 3. Let X1, ..., Xn be a random sample from the N(ux, oî) distribution, and let Y1, ... , Ym be a random sample

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т 2 = d- 3. Let X1, ..., Xn be a random sample from the N(ux, oî) distribution, and let Y1, ... , Ym be a random sample from the N(uy, og) distribution that is independent of the X;'s. Here, Mx, My, ož, and og are unknown. Define 1 = of log: (a) Find a size a test for Ho = lo versus Hį # le based on the statistic {1=1(X; - X)/1=1(Y; - Y)? (b) Based on the test in (a), find a (1 – a) confidence interval for d. (c) Suppose that jy is known. Find a (1-a) confidence interval for based on a different statistic than that in (a). 1