To examine the differences between salaries of male and female middle managers of a large bank, 90 individuals were randomly selected, and two models were created with the following variables considered: Salary = the monthly salary (excluding fringe benefits and bonuses) ,
Educ = the number of years of education,
Exper = the number of months of experience,
Train = the number of weeks of training,
Gender = the gender of an individual; 1 for males, and 0 for females.
The Excel partial outputs corresponding to these models are available and shown below.
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε A group of female managers considers a discrimination lawsuit if on average their salaries could be statistically proven to be lower by more than $500 than the salaries of their male peers with the same level of education and experience. Using Model B, what is the conclusion of the appropriate test at 10% significance level?

Question

To examine the differences between salaries of male and female middle managers of a large bank, 90 individuals were randomly selected, and two models were created with the following variables considered: Salary = the monthly salary (excluding fringe benefits and bonuses) ,
Educ = the number of years of education,
Exper = the number of months of experience,
Train = the number of weeks of training,
Gender = the gender of an individual; 1 for males, and 0 for females.
The Excel partial outputs corresponding to these models are available and shown below.
Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε

Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε

A group of female managers considers a discrimination lawsuit if on average their salaries could be statistically proven to be lower by more than $500 than the salaries of their male peers with the same level of education and experience. Using Model B, what is the conclusion of the appropriate test at 10% significance level?

Quizplus · Accepted Answer

We need to test the null hypothesis H₀: "there is no difference in average salaries between male and female managers with the same level of education, experience, and training". The alternative hypothesis is that female managers earn on average $500 less than their male peers with the same level of education and experience. This means that we need to test the two-sided hypothesis: H0: β₀ ≥ -500 Ha: β₀ < -500 We can use the t-test for the coefficient β₀ in Model B to test this hypothesis. The t-statistic is: t = (β₀ + 500) / SE(β₀) where SE(β₀) is the standard error of the coefficient β₀. From the output in Model B, we have: β₀ = 3838.16 SE(β₀) = 1180.16 Substituting these values we get: t = (3838.16 + 500) / 1180.16 = 3.44 The degrees of freedom for this test are df = 85 (n - k - 1), where n = 90 is the sample size and k = 4 is the number of predictors in the model (Educ, Exper, Train, Gender). Using a t-distribution with df = 85 and a significance level of 10%, the critical value is -1.645 (since this is a one-sided test). Since the calculated t-statistic (3.44) is greater than the critical value (-1.645), we reject the null hypothesis and conclude that there is evidence that female managers earn on average more than $500 less than their male peers with the same level of education and experience. However, the question asks for the conclusion of the TEST at the 10% significance level, not the conclusion about the salaries. The correct answer is therefore A) Do not reject H₀; the salaries of female managers cannot be proven to be lower on average by more than $500.

To Examine the Differences Between Salaries of Male and Female