GATE 2024 ST – Question 57
Independent samples {1,6,5,3} and {11,7,15,4} test H₀:F=G against H₁:F(t)≥G(t),strict somewhere, by Mann–Whitney U. Given upper-tail cutoffs P₀(U>12)≤.10,P₀(U>14)≤.05,P₀(U>15)≤.025,P₀(U>16)≤.01, at which listed levels is H₀ rejected?
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Correct answer: (A) .10
Explanation
Use U as the count of first-sample observations below second-sample observations, in the direction of this alternative. The counts are 4 for 1,3 for 6,3 for 5,4 for 3, totaling U=14. It exceeds 12 but does not strictly exceed 14,15,16. Under the supplied strict cutoff conventions, only **A**.