A Wilcoxon rank sum test for comparing two independent samples involves two samples of sizes 5 and 8. The alternative hypothesis is that the location of population 1 is different from the location of population 2. Using the 0.10 significance level, the appropriate critical values are 21 and 49.

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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 5 and 8 at a 0.10 significance level, the critical values would not be 21 and 49. These values need to be looked up in a Wilcoxon rank sum test table or calculated using statistical software.

A Wilcoxon Rank Sum Test for Comparing Two Independent Samples