Question 1

474 rows, 5 columns

Question 2

Gender, Current Salary, Years of Education, Minority Classification and Date of Birth

Question 3

116 rows, 5 columns

Question 4

The null hypothesis is that mean salary does not differ by sex in the sample population.

Question 5

Because this means that this variable held constant. Therefore, the salaries can be observed knowing that education years, which has a large impact on job opportunities and salaries, is not impacting the t-test results.

Question 6

The t-statistic is 5.0443.

Question 7

The p-value is 1.977e-06

Question 8

The 2.5% lower limit is $3930.78 difference and the upper 2.5% limit is $9024.88 difference.

Question 9

No, the 95% CI does not include the value 0.

Question 10

The mean salary for men is $33527.83 and for women $27050.00

Question 11

The null hypothesis can be rejected with 95% confidence that the salary difference between men and women is between $3930.78 and $9024.88.

Question 12

The t-statistic is 2.4432

Question 13

The p-value is 0.01755

Question 14

The 2.5% lower limit is $664.49 difference and the upper 2.5% limit is $6673.25 difference.

Question 15

No, the 95% CI does not include the value 0.

Question 16

The mean salary for non-minority is $32507.33 and for minority is $28838.46.

Question 17

The null hypothesis can be rejected with 95% confidence that there is a salary difference between non-minority and minority employees and that this difference is between $664.49 and $6673.25.

Question 18

Yes, there is a significant difference in salaries between non-minority men and and minority men at 95% CI. This is because the p-value is 9.209e-08, making it extremely unlikely that the relationship of non-minority men earning higher salaries than minority men occurred by chance.

Question 19

Yes, there is a significant difference in salaries between non-minority women and and minority women at 95% CI. This is because the p-value is 5.478e-05, making it very unlikely that the relationship of non-minority women earning higher salaries than minority women occurred by chance.

Question 20

Mean Salaries Male Female
Non-minority $44,475.41 $26,706.79
Minority $32,246.09 $23,062.50

Question 21

attach(empnum_15years)
interaction.plot(Gender, `Minority Classification`, `Current Salary`)

The interaction plot shows how the mean salary differs based on gender, with the dashed line representing non-minority and solid line representing minority. It tells that the salaries are consistently higher for non-minority employees with 15 years of education than minority equivalents. The positive slope on both of the lines means that non-minorities and minorities have men earning higher salaries than women. The diverging nature of the dashed (0) and solid (1) lines illustrates a strong interaction between the two variables, where the gap between non-minority and minority grows even larger for men.