A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples,one from each population,shown in the following table: She uses the Mann-Whitney U test and a significance level of 0.05.Then σ_U is ______. A) 10.055 B) 11.025 C) 11.255 D) 12.025 E) 12.255

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To use the Mann-Whitney U test, we need to calculate the U statistic for each sample and then use the smaller value as the test statistic. For sample 1: Rank the scores: 15, 16, 18, 20, 23 1, 2, 3, 4, 5 U1 = n1n2 + n1(n1+1)2 − R1 = 5(5) + 5(5+1)2 - 15 = 10 For sample 2: Rank the scores: 11, 12, 13, 15, 18 1, 2, 3, 4, 5 U2 = n1n2 + n2(n2+1)2 − R2 = 5(5) + 5(5+1)2 - 12 = 13 The smaller U value is U1 = 10. Next, we need to find the critical value of U at α = 0.05 with n1 = 5 and n2 = 5: Uα = n1n2.α2 = 12 Since U1 < Uα, we reject the null hypothesis that the means of the two populations are equal. Finally, we can calculate the standard error of the difference between the means using: σ_U = √(n1n2(n1+n2+1)12) = √(5*5*11/12) ≈ 11.255

A Researcher Wants to Determine Whether the Means of Two