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Q57Section ST (Statistics (Q11–Q65))57 of 65

Mann-Whitney decision from tail bounds

Let {1,6,5,3}\{1,6,5,3\} and {11,7,15,4}\{11,7,15,4\} be realizations of two independent random samples of size 4 from two separate populations having cumulative distribution functions F(⋅)F(\cdot) and G(⋅)G(\cdot), respectively, and probability density functions f(⋅)f(\cdot) and g(⋅)g(\cdot), respectively. To test H0:F(t)=G(t)H_0: F(t) = G(t) for all tt, against H1:F(t)≥G(t)H_1: F(t) \ge G(t) with strict inequality for some tt, let UMWU_{MW} denote the Mann-Whitney U-test statistic. Let, under H0H_0, P(UMW>12)≤0.10P(U_{MW} > 12) \le 0.10, P(UMW>14)≤0.05P(U_{MW} > 14) \le 0.05, P(UMW>15)≤0.025P(U_{MW} > 15) \le 0.025 and P(UMW>16)≤0.01P(U_{MW} > 16) \le 0.01. Then, based on the given data, which of the following statements is/are true?

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