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

(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 = a Xi , 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)
⎫
⎬
⎭ = 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.