Please help with the attached question:

Suppose we have a model Yl1, Y12, . .., Yini N ( (1, ? ). Y21, Y22, . .., Y2n2 iid N (12, 02), Y31, Yaz, . .., Yana iid N(/43, 02). Let n = n1 + n2 + n3 and n12 Y1 = _ Yzi, Y3 = n1 i=1 j=1 n3 1 1 An estimate of the common variance of is the pooled variance 3 n - 3 izl j=1 Show that the ratio Y1 - Y 2 ru tn-3 Spy 1 + 7 7 n1 has the t-distribution with n - 3 degrees of freedom. Hint: You may use without proof that SSE P Xn-3 02