CONFIDENCE INTERVAL FOR m_d

To compare the starting salaries of male and female college graduates, an experiment is conducted in which matched pairs of male and female graduates are selected. Each pair of graduates is formed by picking a male and a female with the same major and similar grade-point averages. A random sample of eight such pairs is selected, and the starting annual salary of each person is recorded. These values are in the table below.

Form a 99% confidence interval for the mean difference between the starting salaries of all male and female graduates.

Since matched pairs of observations were selected, these samples are dependent. The parameter of interest is m_d, the mean difference between the starting salaries of all male and female graduates. The formula that needs to be calculated to find the desired interval is

Calculations from StatCrunch: -104.03 to 949.53

Interpretation: I am 99% confident that the mean starting salary for all male graduates could be $104.03 less to $949.53 more than the mean starting salary of all female graduates. (Since this interval contains zero, the mean starting salaries could be equal.)

• This procedure is valid when the population of all possible differences is normally distributed, and a random sample of differences is selected.

• The procedure  in this problem is also valid when a large (30 or more) random sample is selected from any population of all possible differences, regardless of  the original distribution of the differences.

• The usual structure for presenting the solution to a confidence interval was followed. All confidence interval solutions should follow this structure.