Let

Let X1, ..., X/ be i.i.d. Bernoulli random variables with unknown parameter p E (0, 1) . Find a function Tn,, (X,) , which depends on X,, n, and p , such that Tn,p (x , ) - N (0, 1) , M-+00 by using the Central Limit Theorem on Xn and substituting any occurrence of p in the variance by a plug-in estimator for p . (Enter barX_n for Xn). Th.p (Xn) =Select a test with asymptotic level 5% , in terms of the function Tn,p (Choose one for each column.) ( x. ) for each of the following pairs of hypotheses: Ho : p = 0.5 vs H1 : p + 0.5 Ho : P 0.5 Ho : p 2 0.5 vs H1 : p quiz) 1 (ITno5 (X , ) 1-> qu ) 1 (IT .0.5 ( X1 )1-> qu ) 1 (ITno.5 ( X 1 )1> qu ) 1 (Tro5 (X, ) > qu/2 ) 1 (Tho.5 ( X1 ) > qur ) 1 (In.05 (X1 ) > qu ) 1 (In.05 ( X, ) >qu) 1 ( Tho.5 (X ) > qu ) 1 ( Tho.5 (X 1 )