The Distribution of M. 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. (Hint: There are 20 rows.)

b. If the null hypothesis, H0: μ1 = μ2, is true, what percentages of samples will match any given row of the table? (Hint: The answer is the same for all rows.)

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.

Rank 123456 M AAABBB 6 AABABB 7 AABBAB 8

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BBABAA 14 BBBAAA 15