Mathematics · Probability and Statistics
Let (X1, X2, ..., X7) and (Y1, Y2, ..., Y9) be two independent random samples from the continuous distribution functions F(x - μ) and F(x - θ), respectively, where F, μ, and θ are all unknown. Let μ be the unique median of F(x - μ) and θ be the unique median of F(x - θ). Let Ri be the rank of Yi in the combined sample, i = 1, 2, ..., 9. For testing H0: μ = θ against H1: μ > θ, the Wilcoxon rank-sum test statistic T = ∑i=19 Ri is proposed. Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Under H0, P(R1 = 1, R9 = 16) = 1240✓
- 2Under H0, E(T) = 76
- 3Right-tailed test based on T is appropriate for testing H0 against H1
- 4The maximum possible value of T is 115
Correct answer
Under H0, P(R1 = 1, R9 = 16) = 1240
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