(i) Let X1,...,Xn be independently distributed as N(, 2), and let = /. The lower confidence...

(i) Let X1,...,Xn be independently distributed as N(ξ, σ2), and let θ = ξ/σ. The lower confidence bounds θ for θ, which at confidence level 1−α are uniformly most accurate invariant under the transformations X

i = aXi, are

θ = C−1

√nX¯ (Xi − X¯)2/(n − 1)

where the function C(θ) is determined from a table of noncentral t so that Pθ

/ √nX¯ (Xi − X¯)2/(n − 1) ≤ C(θ)

0

= 1 − α.

(ii) Determine θ 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 − α = .95.