3.10.B—Justify the appropriateness of constructing a confidence interval for the difference between two population…

Justify the appropriateness of constructing a confidence interval for the difference between two population proportions by verifying conditions.

• A two-sample z-interval 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 t N11 10≤ % and n ula N22 10≤ % , where N1 is he size of pop tion 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—the number of observed successes, n p1 1  and n p2 2  , and number of observed failures, n p1 11  and n p2 21  , for both samples are all at least 10.