A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 6 and 9. The alternative hypothesis is that the location of population 1 is to the left of the location of population 2. Using the 0.05 significance level, the appropriate critical values are 31 and 65.

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The critical values for a Wilcoxon rank sum test depend on the sample sizes and the significance level. For sample sizes of 6 and 9 at a 0.05 significance level, the critical values would be different from 31 and 65.

A Wilcoxon Rank Sum Test for Comparing Two Independent Samples