5 . Does Ephemeral Products, Inc., practice sex discrimination in determining

employee salaries?

A random sample of twenty employee records produces the following table. The sample is taken by selecting every 30th employee file from a cabinet containing 650 employee records, starting from the 10th file. In addition to salary (in thousands), we write down each employee's age, year of experience, gender (coded as a binary variable: 1 = male, 0 = female), and years of college education (coded 6 = master's degree, 4 = bachelor's degree, 2 = associate's degree, 0 = no college degree). Data are stored in file 'SALARY.MTW'.

Profile of twenty employees of Ephemeral Products }

NAME SALARY AGE EXP GEND EDUC

C6 C1 C2 C3 C4 C5

Mary 22 20 0 0 6

Brenda 37 31 4 0 6

Alicia 60 44 14 0 4

Tom 22 20 0 1 4

Nicole 76 55 25 0 2

Bill 56 44 14 1 0

Gillian 32 25 5 0 6

Bob 80 55 25 1 2

Vivian 68 50 20 0 4

Cecil 86 60 30 1 0

Barney 55 40 15 1 2

Jack 91 64 29 1 0

Wanda 45 35 10 0 6

Sam 83 64 19 1 2

Saundra 55 40 15 0 4

Pete 37 31 4 1 4

Steve 32 25 5 1 6

Fred 45 35 10 1 2

Dick 80 60 21 1 2

Lee 70 50 20 1 2

(5.a) Plot salary against sex. Does the plot indicate any difference of salary due to gender? (Pull down Menu: Graph, Scatter Plot, Simple, choose Y=c1, X=c4)

(5.b) Consider the regression model

\[Salary={{\beta }_{0}}+{{\beta }_{1}}GEND+e\] (5.1)

Test the hypothesis

\[{{H}_{0}}:{{\beta }_{1}}=0\] against \[{{H}_{1}}:{{\beta }_{1}}>0\] at 5% level of significance.

(5.c) Plot the residuals of the above analysis against age, experience and education variables respectively. What can you conclude from these plots?

(5.d) Fit another regression model by including all the available variables:

\[Salary={{\beta }_{0}}+{{\beta }_{1}}GEND+{{\beta }_{2}}EXP+{{\beta }_{3}}AGE+{{\beta }_{4}}EDUC+e\] (5.2)

(5.e) Check the adequacy of this model.

(5.f) Test the hypothesis

\[{{H}_{0}}:{{\beta }_{1}}=0\] against \[{{H}_{1}}:{{\beta }_{1}}>0\] at 5% level using results in (5.d).

(5.g) Make a list of the "overpaid" employees (large positive residual) and ’underpaid’ employees (large negative residual). (print residuals and name (C6))

(5.h) Combine results in (5.b), (5.f) and (5.g). What is your conclusion for the question raised in the beginning? Explain.

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