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.

First test (male) = (female) to determine if data should be pooled.

Following the 4 step hypothesis process.

Step 1:
Ho:  (male) = (female), Yes pool variances.
H1:  (male) not equal (female), No do not pool variances.

Step 2:
The level of significance is 0.05

Step 3:
Use the 2-SampFTest to calculate the p value.

1.  Choose "STAT".   2.  With "EDIT" highlighted select "1:Edit" by pressing "ENTER".   3.  If there is data in List 1 (L1) clear it by using the up arrow to highlight "L1".  Then press "CLEAR" and "ENTER".          Repeat Step 3 to clear data from List 2 (L2).   4.  Enter the "Male Managers" into List 1 (L1) by entering each value and pressing "ENTER" after each value.   5.  Use the arrow keys to move the cursor to List 2 (L2).  Enter the "Female managers" into List 2 (L2) by         entering each value and pressing "ENTER" after each value.   6.  Press the buttons "2nd" and "MODE" (QUIT) to signify the end of the data.   7.  Choose "STAT".  Use the right arrow to highlight "TESTS".  8.  Use the down arrow to choose "D:2-SampFTest" and press "ENTER".  9.  Use the arrow key to highlight "Data" and press "ENTER".  10.  Use the down arrow and press "2nd" "1" to submit  (L1) as List 1.  11.  Use the down arrow and press "2nd" "2" to submit  (L2) as List 2.  12.  Press "ENTER" to accept Freq1: 1  13.  Press "ENTER" to accept Freq2: 1  14.  Use the arrow keys to highlight the status of the "Alternate Hypothesis", in this case H1:   1 2  15. Use the down arrow to highlight "Calculate" and press "ENTER".  16.  Since the = case is used, the p-value must be divided by 2,  p = 0.4827.

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

Independent Test for two sample means.
Step 1:
H₀: Mean (men) - Mean (women) < 0 
H₁:  Mean (men) - Mean (woman) > 0 claim

Step 2:  

Step 3:
Using 2-SampTTest to calculate the p value.

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:
H₀: Mean (men) - Mean (women) < 0 
H₁:  Mean (men) - Mean (woman) > 0 claim

Step 2:  

Step 3:
Using the T-Test to calculate the p value.

1.  Subtract List 1 from List  2, Enter L1 ("2nd", "1") "-" L2 ("2nd",  "2") and press "ENTER".   2.  Store the differences in L3 by entering "STO", "2nd", "3" and press "ENTER".   3. Choose "STAT".  Use the right arrow to highlight "TESTS".   4.  Use the down arrow to choose "2: T-Test" and press "ENTER".    5.  Use the right arrow to highlight "Data and press "ENTER".    6.  Use the down arrow and enter the value 0 for the population mean, , and press "ENTER".    7.  Enter the value L3 ("2nd", "3") for List, and press "ENTER".    8.  Enter the value 1 for "Freq" and press "ENTER".    9.  Use the arrow keys to highlight the status of the "Alternate Hypothesis", in this case µ: > .    10.  Use the down arrow to highlight "Calculate" and press "ENTER".     11.  The p-value is approximately 0.0086.

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.

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