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Statistics: Hypothesis and Sampling

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EXHIBIT 1: A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0=female, 1=male) and job type (0=clerical, 1=technical). The following tables summarizes the regression results:

df SS MS F
Regression SS 3 1004346.771 334782.257 5.96
Unexplained SS 26 1461134.596 56197.48445

Coefficients Standard Error t Stat P-Value
Constant 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
Gender 222.78 89.00 2.50 0.02
Job -28.21 89.61 -0.31 0.76

(A) Referencing Exhibit 1, based on the SS table and 0.05 significance level, the global null hypothesis test of the multiple regression model (2 points):
(a) Will be rejected and conclude that monthly salary is related to all the independent variables
(b) Will be rejected and conclude that monthly salary is related to at least one of the independent variables
(c) Will not be rejected
(d) Will show a high multiple coefficient of determination
(e) Cannot be ascertained given the above information

(B) Referencing Exhibit 1, the adjusted multiple coefficient of determination is (3 points):
(a) 5.93%
(b) 59.3 %
(c) 40.7 %
(d) 33.9%
(e) None of the above

(C) Referencing Exhibit 1, based on hypothesis tests for the individual regression coefficients at a 5% significance level (2 points),
(a) All the regression coefficients are not equal to zero.
(b) "Job" is the only significant independent variable in the model.
(c) Only "Service" and "Gender" are significantly related to monthly salary.
(d) "Service" is the only significant variable in the model.
(e) None of the variables are significant

(D) Referencing Exhibit 1, which of the variables are dummy variables in the model (2 points)?
(a) Salary
(b) Service
(c) Service and gender
(d) Gender and job
(e) Service, gender and job

(E) Referencing Exhibit 1, the results for the variable "Gender" show (2 points)
(a) Males average $222.78 more than females in monthly salary
(b) Females average $222.78 more than males in monthly salary
(c) Gender is not related to monthly salary
(d) Gender and months of service are correlated

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