Let (X1, Y1), , ,(Xn, Yn) be a random sample from a bivariate normal distribution with parameters Icirc frac14 x, Icirc frac14 Y, p We are interested in testing H0 Icirc frac14 x Icirc frac14 Y versus H1 Icirc frac14 x Icirc frac14 Y (a) Show that the random variables Wi Xi Yi are iid n( Icirc frac14 w, Iuml 2w) (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 ) Tw M,

Question: Let (X1, Y1),...,...,(Xn, Yn) be a random sample from a bivariate normal distribution with parameters Î¼x,Î¼Y, p. We are interested in testing H0: Î¼x =

Let (X1, Y1),...,...,(Xn, Yn) be a random sample from a bivariate normal with parameters Î¼x,Î¼Y, p. We are interested in testing
H0: Î¼x = Î¼Y versus H1: Î¼x ‰ Î¼Y.
(a) Show that the random variables Wi = Xi - Yi are iid n(Î¼w,Ïƒ2w).
(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.)

Tw M,

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