53. (i) Let XI' .. " X; be independently distributed as N(t 0 2), and let 8 = ~jo The lower confidence bounds for 8, which at confidence level 1 - a are uniformly most accurate invariant under the transformations Xi = aX;, are 8 = CI( .[nX ) - VE(X;-X)2j ( n - l ) where the function C(8) is determined from a table of noncentral t so that ( .[nX ) Ps C(8) = 1 -

a. VE(X; - X)2 j(n -1) (ii) Determine when the x's are 7.6, 21.2, 15.1, 32.0, 19.7, 25.3, 29.1, 18.4 and the confidence level is 1 - a = .95.