The File name HARRIS7 shows the values of the following variables for randomly selected 93 employees of Harris Bank Chicago in 1977. (This real data set was used in a court lawsuit.) y = starting monthly salary in dollars (SALARY), x1 = years of schooling at the time of hire (EDUCAT), x2 = number of months of previous work experience (EXPER), x3 = number of months after January 1, 1969, that the individual was hired (MONTHS), x4 = indicator variable coded 1 for males and 0 for females (GENDER).
1. What are the sample average and the sample standard deviation of the starting salary of the selected male employees? What are the sample average and the sample standard deviation of the starting salary of the selected female employees? (The Excel instructions for computing descriptive statistics are on pages 145 â 146.)
2. Let μ1 = the average starting salary for all male employees, and μ2 = the average starting salary for all female employees. What are the 95% confidence intervals for μ1 and μ2? (The Excel instructions for computing descriptive statistics, including the margin of error for a specified confidence level, are on pages 354 â 356. (Remember that any confidence interval must have two ends, and that Excel shows the margin of error for a given confidence level rather than the confidence level or confidence interval.)
3. Conduct the hypothesis test to determine whether , that is, there is evidence of wage discrimination for the Harris Bank employees. Use a 5% level of significance. State the two hypotheses to be tested, the H0 rejection rule under the critical value approach, the value of the test statistic, the p-value of the test, your conclusion and its interpretation. (Assume unequal population variances; see Excel instructions on page 446 - 447.)
Regression analysis has been used increasingly in employment discrimination cases. Evidence of lower average starting salary can provide some support for a discrimination suit against the employer. It is recognized, however, that a simple comparison of mean starting salaries (the test you conducted in 3) might be insufficient to conclude that the female employees have been discriminated against. Obviously there are other factors that affect the starting salary to which differences in the average starting salary might be attributed. These factors have been identified as x1, x2 and x3 defined above. Assume the following regression model, y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε, and apply Regression in Data Analysis of Excel (See Excelâs instructions on pages 618 - 619)
4. What is the estimated regression equation? Assuming that the values of x1, x2 and x3 are fixed, what is the predicted average difference between the male and female starting salaries?
5. At a 5% significance level, conduct the F test for the overall significance of the regression model. State the two hypotheses to be tested, the H0 rejection rule under the critical value approach, the value of the test statistic, the p-value of the test, your conclusion and its interpretation.
6. Is there a difference in the average starting salaries for male and female employees after accounting for the effects of the three other independent variables? Use a 5% level of significance to answer this question. State the two hypotheses to be tested, the H0 rejection rule under the critical value approach, the value of the test statistic, the p-value of the test, your conclusion and its interpretation.
7. What starting salary would you forecast, on average, for a male employee with 12 years educations, 10 months of previous work experience, and with time hired equal to 15 months?
8. What starting salary would you forecast, on average, for a female employee with 12 years educations, 10 months of previous work experience, and with time hired equal to 15 months?