Suppose X1,.... Xn are iid N(p, 0?). In the week 7 Tutorial it was noted that the statistic Y = (n- 1)52 = EL,(X - X)? (where X = _ _ _, X; and $2 are the sample mean and variance) has 'Xn-1 distribution (note we are not multiplying by - as we did in the week 7 Tutorial!). Consider testing Ho: 02 = 1 against H1: 02 # 1. (1) 1. One possible level-a test is the "equal-tailed" test based on Y, where we reject for Y b where Poly b) = ?. (a) Taking a = 0.04 and n = 5, find appropriate values a and b. (b) Defining sig . sq= (50: 150)/100 plot the power of the test against sig. sq. Add a horizontal dotted line to indicate the level. 2. In Tutorial week 7 we also saw that the UMPU test rejects for large values of $2 - log($2) which is equivalent to rejecting for small values of the statistic T = (n - 1) log Y - Y ; to see this, write log(S") = log Y - log(n - 1), multiply through by n - 1 and ignore the (n - 1) log(n - 1) term. If the test is to have level o, we reject for Y