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.

Excel partial outputs corresponding to these models are available and shown below.

Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε

	df	SS	MS	F
Regression	4	28,045,960.12	7,011,490.03	43.23
Residual	85	13,787,729.88	162,208.59
Total	89	41,833,690.00
	Coefficients	Standard Error	t-stat	p-value
Intercept	4,663.31	365.37	12.76	1.85E-21
Educ	140.66	20.15	6.98	6.07E-10
Exper	3.36	0.47	7.17	2.54E-10
Train	1.17	3.72	0.31	0.7543
Gender	615.15	97.33	0.32	1.16E-08

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

	df	SS	MS	F
Regression	3	28,029,969.88	9,343,323.29	58.21
Residual	86	13,803,720.12	162,508.37
Total	89	41,833,690.00
	Coefficients	Standard Error	t-stat	p-value
Intercept	4,713.26	327.1967	14.40	1.21E-24
Educ	139.54	19.7253	7.07	3.78E-10
Exper	3.35	0.4649	7.20	2.10E-10
Gender	609.25	94.9920	6.41	7.39E-09

A group of female managers considers a discrimination lawsuit if on average their salaries can 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 alternative hypothesis for testing the lawsuit condition?

• H_A:β₃>500

• H_A:β₃ ≠ 500

• H_A:β₃≤500

• H_A:β₃<500

Answer 1

Solution: Obtain the correct option. In the given scenario, the claim is that the salary for female managers is less than S500 from its peers males managers, given all the other variables are held constant. Thus, the correct choice for the alternative hypothesis is, H P <500 Therefore, the correct option is the last option from the beginning