Mathematics · Probability and Statistics
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?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Reject H0 when X1 > 1 - α
- 2Reject H0 when X(n) > (1 - α)1/n
- 3Reject H0 when X(n) < (1 - α)1/n✓
- 4Reject H0 when X(1) > 1 - α1/n
Correct answer
Reject H0 when X(n) < (1 - α)1/n
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