3.12.C—Justify the appropriateness of a hypothesis test for the difference between two population proportions by…

Justify the appropriateness of a hypothesis test for the difference between two population proportions by verifying conditions.

• A two-sample z-test for a difference between two population proportions requires that three conditions be met:
  • i. The randomization condition—the data should be collected using two independent random samples or a randomized experiment.
  • ii. The 10% condition—when sampling without replacement, the size of each sample should be less than or equal to 10% of the respective population size: n s t N11 10% and n2 ulati N210% , where N1 i he size of pop on 1 and N2 is the size of population 2. The sample sizes are represented as n1 and n2. (Note: This condition is unnecessary when the data are from a randomized experiment.)
  • iii. The normality condition—n pc1 , n pc1 1  , n pc2  , and n pc2 1  , must all be at least 10, with p np np nn c   1 1 2 2 12 being the combined (or pooled) proportion assuming that H0 is true (H01: pp 2 or H:01 pp 2 0). Inference for Categorical Data: Proportions UNIT 3 108