Connecting Tests and Intervals: Apply It 1

  • Explain how a confidence interval is related to a two-sided hypothesis test.

Labor Market Discrimination

Recall the 2004 study by two University of Chicago economists who wanted to test for labor market discrimination. The investigators created [latex]4,890[/latex] mock identical resumés, which were sent to job placement ads in Chicago and Boston. To gauge market racial discrimination, each resumé was randomly assigned either a commonly-white or commonly-black name. The experimenters then measured the proportion of resumés from each group (white and black) that received callbacks.

The results are summarized in the following table:

  Commonly-White Names Commonly-Black Names Total
Called back [latex]246[/latex] [latex]164[/latex] [latex]410[/latex]
Not called back [latex]2199[/latex] [latex]2281[/latex] [latex]4480[/latex]
Total [latex]2445[/latex] [latex]2445[/latex] [latex]4890[/latex]

Let [latex]p_1[/latex]= true proportion of commonly-white named resumés that receive a callback.

Let [latex]p_2[/latex]= true proportion of commonly-black named resumés that receive a callback.