Two-Sample Test for Proportions: Learn It 2

  • Recognize when a one-sample [latex]z[/latex]-test or a two-sample [latex]z[/latex]-test is needed to answer a research question.
  • Complete a two-sample [latex]z[/latex]-test for proportions from hypotheses to conclusions.

Will I get a callback?

Scenario:

In 2004, two University of Chicago economists (Marianne Bertrand and Sendhil Mullainathan) decided to conduct an experiment[1] 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.[2]

The steps and the logic of the hypothesis test for comparing two population proportions are the same as we are conducting a hypothesis test for a population proportion.

We will need to: Write the null and alternative hypotheses, collect the data and check its conditions, assess the evidence (calculate its test statistics, find the p-value, compare p-value with the significance level), and state its conclusion.

  1. Bertrand, M. & Mullainathan, S. (2003, July). Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. National Bureau of Economic Research. https://www.nber.org/papers/w9873 ↵
  2. Lesson adapted from Skew The Script. https://skewthescript.org/7-8 ↵