Project: Two means Revisited.

Project: Management Attacks Labor's Defense.

Scenario:
In a previous project, a jury was given the task of determining if female managers earned less than their male counterparts. The jury was presented with
A. The salaries of 40 managers (20 male and 20 female).

Female	Male
$43,800	$44,000
$35,500	$36,000
$39,700	$38,000
$38,000	$42,000
$36,500	$37,000
$33,000	$35,000
$54,000	$56,000
$36,000	$36,000
$54,000	$53,000
$35,500	$36,000
$34,900	$38,000
$36,900	$38,000
$47,800	$50,000
$42,000	$45,500
$30,000	$31,000
$42,000	$41,500
$39,000	$38,500
$42,500	$42,000
$31,000	$31,000
$38,000	$39,500

B. Management used independent testing of two means to show that the mean pay of female
     managers was not less than their male counterparts.
C. Labor used dependent (paired data) to show that the mean pay of female managers was less
     than their male counterparts.
D. Since the data was paired according to experience, responsibilities, etc, gender was the only
     difference being measured. The jury believes that the females are getting paid less then
     their male counterparts.

Management's Attack
In an effort to discredit labor's defense, management argues labor used an illegitimate test and therefore their conclusion is invalid. A prerequisite for hypothesis testing of dependent (paired) data requires that the sample size be large (at least 30) OR the differences are Normally distributed with no outliers.

Project:
I. Normal Probability Plot
    A. Find the differences for the paired data (Female, L1 - Male managers, L2). Store the differences
         in L3.
    B. Sort the differences (L3) in ascending order.
          1. Press "STAT".
          2. Select "2:SortA(".
          3. Enter "2nd", "3)", for List 3.
          4. Press "ENTER".
    C. Using List 3, fill in the table, this will be the x coordinate.
    D. Use the Normal Probability Plot to find the standard score associated with the differences of
         the paired data (L3). This will be the y coordinate. Fill in the table.

II. Show all four steps of the hypothesis test process. Test at a 0.05 level of significance whether the
differences are Normally distributed. Is the straight line a legitimate model for the differences?
If so, then the differences are Normally distributed?

III. Based on your hypothesis tests, should the jury believe Management or Labor? Explain
your decision.