Solutions: Two Means

POINT: Management presents their case as two independent means. Show all four steps for each hypothesis test needed to test the following claim: "The mean pay of the female managers is less than their male counterparts." At the 0.05 level of significance, test whether the following corporation is guilty of "gender discrimination" in the manner they pay their employees.

I. No effort was made in pairing the data. Perform the hypothesis tests using the Female and Male data as
Independent Data.
Note: Remember to hypothesis test

(male) =

(female) to determine if the variances should
be pooled or not when testing the means.

Step 1:
Ho:

(male) =

(female), Yes pool variances.
H1:

(male) not equal

(female), No do not pool variances.

1. Enter the data for the female managers into Column 1, label it Female.
2. Enter the data for male managers into Column 2, label it Male.
3. Click on “Stat” at the top of the screen.
4. Then select “Basic Statistics” from the menu that appears.
5. Choose "Display Descriptive Statistics".
6. Select "Female" by clicking on "C1 Female" and then select “SELECT” at the bottom of the screen.
7. Select "Male" by clicking on "C2 Male" and then select “SELECT” at the bottom of the screen.
8. Select "OK". The sample standard deviation (sx) for "Female" is $6,570. The sample standard deviation (sx)
     for "Male" is $6,636. The F-test requires the larger standard deviation becomes the numerator.  Comparing
     standard deviations, the larger standard deviation is in Male, this will be the first data set.
9. Then select “2 Variances” from the menu that appears.
10. On the new window, “2 Variances”, select "Samples in different columns".
11. Then put the cursor into the "First" rectangle.
12. Select "Male" by clicking on "C2 Male" and then select “SELECT” at the bottom of the screen.
13. The cursor moves to the "second" rectangle. Select "Female" by clicking on "C1 Female" and then select “SELECT”
       at the bottom of the screen.
14. Select "OK".
15. Ignore the confidence intervals. The p-value for the F-Test is approximately 0.965. Since the = case is used, the
       p-value must be divided by 2, p is approximately 0.4825.

Step 4:
"Fail to Reject the Null Hypothesis. Yes, pool the variances., they are equal.

Independent Test for two sample means.
Step 1: Using the same arrangement used for the F-test.
H₀: Mean (men) - Mean (women) < 0
H₁: Mean (men) - Mean (woman) > 0 claim

1. Click on “Stat” at the top of the screen.
2. Then select “Basic Statistics” from the menu that appears.
3. Then select “2-Sample t” from the menu that appears.
4. On the new window, “2-Sample t (Test and Confidence Interval)”, select "Samples in different columns".
5. Then put the cursor into the "First" rectangle.
6. Select "Male" by clicking on "C2 Male" and then select “SELECT” at the bottom of the screen.
7. The cursor moves to the "second" rectangle. Select "Female" by clicking on "C2 Female" and then select “SELECT”
at the bottom of the screen
8. Select the "Assume equal variances" square.
9. Select "Options". Enter "0" into "Test difference" and select "Greater Than" as the "Alternative" choice.
10. Select "OK".
11. Select "OK".
12. The p value is approximately 0.335.

Step 4:
Fail to Reject the Null Hypothesis.
Claim is NOT supported. The data shows that females do not earn less than males.

COUNTERPOINT: Labor presents their case as two dependent means. Every effort was made in pairing the data (same amount of experience, same responsibilities, etc.). Show all four steps for each hypothesis test needed to test the following claim: "The mean pay of the female managers is less than their male counterparts." At the 0.05 level of significance, test whether the following corporation is guilty of "gender discrimination" in the manner they pay their employees.

Dependent Test for two sample means.
Step 1: Using the same arrangement used for the F-test.
H₀: Mean (men) - Mean (women) < 0
H₁: Mean (men) - Mean (woman) > 0 claim

1. Click on “Stat” at the top of the screen.
2. Then select “Basic Statistics” from the menu that appears.
3. Then select “Paired t” from the menu that appears.
4. On the new window, “Paired t (Test and Confidence Interval)”, select "Samples in columns".
5. Then put the cursor into the "First" rectangle.
6. Select "Male" by clicking on "C2 Male" and then select “SELECT” at the bottom of the screen.
7. The cursor moves to the "second" rectangle. Select "Female" by clicking on "C2 Female" and then select “SELECT”
at the bottom of the screen
8. Select "Options". Enter "0" into "Test difference" and select "Greater Than" as the "Alternative" choice.
9. Select "OK".
10. Select "OK".
11. The p value is approximately 0.009.

Step 4:
Reject the Null Hypothesis.
Claim is supported. The data shows that females do earn less than their male counterparts.

III.   Based on your hypothesis tests
        A. Are there grounds for a gender discrimination lawsuit in behalf of the female managers?
              Depends which approach was used.

        B. If you represented management, which approach, independent or dependent, would be
              the basis of your defense?
            Independent.

         C. If you represented labor, which approach, independent or dependent, would be the basis
             of your prosecution?
            Dependent.

D. Which approach should the jury believe? Explain your decision.
Dependent. The paired data made gender the only variable being measured.