Question

We like to test that mean income of town A is higher than that of town B with 0.05 alpha. To test, we collect 15 data from each town. Which one is the correct one? Choose all applied.

a. We need to do Two Shapiro tests first and if both conclusions are not "reject H0", then do Wilcoxon rank sum test with medians to compare.

b. We need to do Two Shapiro tests first and if both conclusions are "Do not reject H0", then do pooled t test if population variances of incomes of two towns are equal.

c. We need to do Two Shapiro tests first and if both conclusions are "Do not reject H0", then do separated t test if population variances of incomes of two towns are equal.

d. We need to do Two Shapiro tests first and if both conclusions are not "reject H0", then do Wilcoxon rank sum test with means to compare.

Answer 1

First we need to check whether two samples come from normal distribution or not. For this, we perform Shapiro test separately. If both conclusions  are "Do not reject H0". Then we can assume that two samples come from two independent normal populations. Now we test whether two population variances are equal or not. If conclusion is two population variances are equal then we perform pooled t test to answer this question. Hence correct option is:

b. We need to do Two Shapiro tests first and if both conclusions are "Do not reject H0", then do pooled t test if population variances of incomes of two towns are equal.

Note that we can perform Wilcoxon rank sum test with medians but it is not better than 2 sample t test under normality condition.