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.

Answer 1

a) Assumptions that satisfies in the above data to run t-test:

1) Data is from normal population, known by using boxplot( code is included in Rscript code):

2) Sample 1 does not dependent on sample 2, known as the males bonus are not dependent on females bonus.

3) Population variance are equal.

R Script code:

Result: