Question

Use R for this problem(Code in R). A firm’s personnel officer sampled 36 male and 24 female employees investigate allegations that the men in the organization tend to receive hire annual bonuses than the women. Their bonuses (as percentages of their annual salaries) are below.

Men

10.4	8.9	11.7	12.0	8.7	9.4	9.8	9.0	9.2	9.7
9.1	8.8	7.9	9.9	10.0	10.1	9.0	11.4	8.7	9.6
9.2	9.7	8.9	9.3	10.4	11.9	9.0	12.0	9.6	9.2
9.9	9.0	9.2	9.4	9.7	8.9

Women

8.4	9.0	9.0	7.7	9.6	8.4	9.1	9.2	8.7	9.1
9.3	8.4	6.7	9.9	8.0	9.2	7.7	11.9	6.2	8.4
9.0	6.9	7.6	7.4

a) Check all necessary assumptions for running a t-test for the difference between the two populations of bonus percentages. If you need to, check normality with boxplots, normal probability plots, ad.test(), and shapiro.test().
b) Can you pool in this situation Why or why not
c) Write down the hypotheses to test given the personnel officer wants to know if there is evidence to conclude the men receive higher bonus percentages. Use R to run a t-test using the t.test() function. Provide your code, output, and conclusion based on the p-value.

Question!

I tested the Anderson-Darling and Shapiro tests. According to the two tests, in case of men, we reject to the null hypothesis since the p-value is too small. So, the population of men don't follow the normal distribution. However, the answers from this website are saying the men is normal distribution. And, do you think is can not be pooled? They are almost same standard deviation. I don't want to get same answer that is from here.

Answer 1