Question

“Learn to Write A Great Country Song” has become the top selling book and Shania wanted to know whether the book worked better for one gender. So Shania asked 10 males and 15 females to spend 14 hours over a week period to write a song using the book. All songs were subsequently ranked, and the sum of ranks for males equaled 77 while the sum of ranks for females equaled 248. Use a Mann-Whitney U test.

In the box below, provide the following information:

Null Hypothesis in sentence form (1 point):

Alternative Hypothesis in sentence form (1 point):  
Critical Value(s) (2 points):

Calculations (4 points): Note: the more detail you provide, the more partial credit that I can give you if you make a mistake.

Outcome (determination of significance or not, effect size if appropriate, and what this reflects in everyday language, 2 points)

Answer 1

The Null Hypothesis: H0: The medians of the 2 populations are equal.

The Alternative Hypothesis: Ha: The medians of the 2 populations are not equal.

The Critical Value: Since is not mentioned, we use the default value of 0.05. The critical value from the Mann Whitney U critical value table for n = 10and n2 = 15 for = 0.05 is 39.

Calculations: The test statistic is calculated as Minimum(U1, U2), where U is the test statistic.

n1 = 10, n2 = 15, R1 = 77, R2 = 248

U1 = n1n2 + [n1(n1 + 1)/2] - R1 = 10 * 15 + [10*(10+1)/2] - 77 = 150 + 55 - 77 = 128

U2 = n1n2 + [n2(n2 + 1)/2] - R2 = 10 * 15 + [15*(15+1)/2] - 248 = 150 + 120 - 248 = 22

Therefore Minimum(U1, U2) = 22

Outcome: The decision rule is Reject H0, if U 39. Since U2 (22) is < 39, we Reject H0 and conclude that the medians of the 2 populations are different.

There is significant evidence at = 0.05 that the book Shania wrote works better for one gender and that it is not equal for both Males and Females.