A loan officer at a bank wishes to compare the new car loan rates charged at banks in Ohio with the new car loan rates of Ohio credit unions. Two independent random samples of bank rates and credit union rates in Ohio are obtained with the following results (all rates are fixed rates):

Because both samples are small, the bank officer is uncertain about the shape of the distributions of bank and credit union new car loan rates. Therefore, the Wilcoxon rank sum test will be used to compare the two types of loan rates.

a. Let D₁ be the distribution of bank rates and let D₂ be the distribution of credit union rates. Carry out the Wilcoxon rank sum test to determine whether D₁ and D₂ are identical versus the alternative that D₁ is shifted to the right or left of D₂. Use α = .05.
b. Carry out the Wilcoxon rank sum test to determine
whether D₁ is shifted to the right of D₂. Use α = .025. What do you conclude?

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Bank Rates: Credit Union Rates: 3.25 2.25 2.75 3.00 2.50 3.00 2.40 2.50 4.25 3.50 3.25 4.00 4.10 3.75 3.50 4.25