statistical questions

Two independent samples X1, ..., Xn and Y1, ..., I'm of iid. observations are drawn from normal distributions /(ux, of) and N(ur, ;) respectively, where the true means Ax, by and the true variances ov, or are unknown. The sample sizes n and m are known constants. As usual, we denote the sample means and the sample variances (respectively) by X=! X and X (X - X) n - and Y =_ Y and S; = (1 - Y)2. m - (a) Give the name and parameters of the exact distribution of the quantity and (for sample sizes n = 16, m = 11) find its 5th and 95th percentiles by using either the provided statistical tables or other resources. 3 pts (b) Hence perform a statistical test, at the 5% significance level, of the null hypothesis Ho :ov = ov against the alternative hypothesis Ha : of