Suppose X1, X2, ..., Xn are i.i.d. random variables uniformly distributed on the interval (0, θ) where θ > 0. Let X(1) ≤ X(2) ≤ ... ≤ X(n) be the corresponding order statistics. For testing the hypotheses H0: θ = 1 versus H1: θ ≠ 1, which of the following tests has a significance level α for 0 < α < 0.5?

Question

Mathematics · Probability and Statistics

Verified Solution4 Options

Answer 1

Reject H0 when X1 > 1 - α

Answer 2

Reject H0 when X(n) > (1 - α)1/n

Answer 3

Reject H0 when X(n) < (1 - α)1/n

Answer 4

Reject H0 when X(1) > 1 - α1/n

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