Question

II. Show all of your work in each question. In parts (d), (e), and (g) make sure to set up your null and alternative hypotheses and write your conclusions. Also, please round your numbers to 2 decimal points. Write legibly and neatly. III. You can use p-value approach or critical-value approach in writing the conclusions of your hypotheses. A large firm employing tens of thousands of workers has been accused of discriminating against its female managers. The accusation is based on a random sample of 40 managers. The mean annual salary of the 20 female managers is $79,500 while the mean annual salary of the 20 male managers is $103,250. The president of the firm points out that the company has a strict policy of equal pay for equal work and that the difference may be due to other variables. Accordingly, he found and recorded the number of years of education and the number of years of experience for each of the 40 managers in the sample. Also recorded are the salary and gender (1 = female and 0 = male). The data are in attached Excel document. The president wanted to know whether a regression analysis would shed some light on the issue. Use Microsoft Excel to run a regression of annual salary on years of education, years of experience, and gender and round up numbers in your regression results to 2 decimal points. Please use the level of significance of 10 percent (i.e. α = 0.10). On the basis of your Excel results answer following questions. (1 pts.) a. Write down the estimated regression equation.

Annual Salary(in $1000.00)	Education(in years)	Experience(in years)	Gender
130	20	18	0
80	19	16	1
62	18	8	1
176	18	30	0
44	14	9	1
139	16	22	0
165	18	27	0
112	19	20	1
92	16	17	1
84	18	13	1
106	14	17	0
103	22	24	1
98	16	18	0
93	17	14	1
79	16	14	1
92	16	14	0
79	14	16	0
98	20	18	1
111	19	25	1
45	15	10	0
82	16	13	0
100	19	21	1
88	15	15	0
76	18	13	1
123	16	21	0
120	17	22	0
50	18	7	1
30	17	4	1
135	16	19	0
84	14	17	0
50	16	6	1
65	15	9	0
83	17	12	1
105	21	21	1
70	17	10	1
99	15	12	0
89	18	8	0
93	15	14	0
68	17	11	1
57	15	10	0

Answer 1

We have used MS Excel to do regression analysis.

Following are screenshot showing steps we followed:

1. Input Data

2. Select Data analysis tool from Data tab

3. Select Regression in Data analysis dialog box

4. Enter required information in Regression analysis dialog box and click Ok to see the output

Following is regression analysis output:

From the output, we can write regression equation as follows:

Annual Salary = -2.899 + 2.485*Education + 4.007*Experience - 18.779*Gender

From the regression coefficient table, we can see that:

1. Experience is an significant predictor of Annual Salary since p value of regression coefficient of experience is less than 0.01

2. Gender is also an significant predictor of Annual Salary since p value of regression coefficient of gender is less than 0.01.

Putting gender = 0 in regression equation, we get regression equation for annual salary for male:

Annual Salary = -2.899 + 2.485*Education + 4.007*Experience

Putting gender = 1 in regression equation, we get regression equation for annual salary for female:

Annual Salary = -2.899 + 2.485*Education + 4.007*Experience - 18.779*1

Based on regression equation, it can be seen that for same level of education and experience females on average earns $18779 less annually in comparison to males. So, it can be said the there is a problem of pay inequality in the company. In other words, males are paid more in comparison to females for same level of education and experience.