Let (X1, Y1),...,...,(Xn, Yn) be a random sample from a bivariate normal distribution with parameters μx,μY, p. We are interested in testing
H0: μx = μY versus H1: μx ‰  μY.
(a) Show that the random variables Wi = Xi - Yi are iid n(μw,σ2w).
(b) Show that the above hypothesis can be tested with the statistic

Where

Furthermore, show
that, under H0, Tw ~ Student's t with n- 1 degrees of freedom. (This test is known as the paired-sample t test.)

Transcribed Image Text:

Tw M,