Problem 1

The dimensions of the data set are 5 x 474.

Problem 2

The variables included in the data set are gender, current salary, years of education, minority classification, and date of birth.

Problem 3

The dimensions of the new data frame are 5 x 116.

Problem 4

The null hypothesis is the hypothesis that there is no relationship between two given sets of data. When accepting the null hypothesis, we believe that any perceived relationship between the variables is due to chance. When rejecting the null hypothesis, we believe that there is indeed a relationship between the two variables.

Problem 5

We are including only samples with 15 years of education to ensure that the education level does not influence the conclusion.

Problem 6

The t-statistic is 5.0443.

Problem 7

The p-value is 0.000001977.

Problem 8

The limits of the 95% confidence interval are 3930.779 and 9024.884.

Problem 9

No, the confidence interval does not include the value zero.

Problem 10

The mean salary for men with 15 years of education is 33,527.83 dollars. The mean salary for women with 15 years of education is 27,050 dollars.

Problem 11

Based on the results of this test, I would reject the null hypothesis and conclude that gender has an influence on salary.

Problem 12

The t-statistic is 2.4432.

Problem 13

The p-value is 0.01755.

Problem 14

The limits of the 95% confidence interval are 664.4916 and 6673.2519.

Problem 15

No, the confidence interval does not include the value zero.

Problem 16

The mean salary for minorities with 15 years of education is 28,838.46 dollars. The mean salary for non-minorities with 15 years of education is 32,507.33 dollars.

Problem 17

Based on the results of this test, I would reject the null hypothesis and conclude that minority status has an influence on salary.

Problem 18

There appears to be a significant enough difference between the salaries of minority and non-minority men based on a 95% confidence interval.

Problem 19

There appears to be a difference between the salaries of minority and non-minority women, but not enough of a difference based on a 95% confidence interval.

Problem 20

Mean Salaries Male Female
Non-Minority $34,489.38 $27,354
Minority $30,055.56 $26,100

Problem 21

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The plot tells you that salaries are higher for men than they are for women regardless of minority status. Additionally, salaries are higher for non-minority individuals than they are for minority individuals, with the difference being more pronounced for men than it is for women.