In this exercise, you are to obtain the distribution of the variable M when the sample sizes are both 3. Doing so enables you to see how the Mann-Whitney table is constructed. All possible ranks for the data are displayed in the following table; the letter A stands for a member from Population 1, and the letter B stands for a member from Population 2.

a. Complete the table.

b. If the null hypothesis, H0: μ1 = μ2, is true, what percentages of samples will match any given row of the table?

c. Use the answer from part (b) to obtain the distribution of M when n1 = 3 and n2 = 3.

d. Draw a relative-frequency histogram of the distribution obtained in part (c).

e. Use your histogram from part (d) to obtain the entry in Table VI for n1 = 3, n2 = 3, and α = 0.10.

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Rank 1 2 3 56 1 2 3 45 6 M A A B A B B 7 BBBA A A 15