4.7.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 means by verifying conditions.

• A two-sample t-interval for a difference between population means 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: n11≤10%N and n22≤10%N , where N1 is the size of population 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 sample data condition—both samples should have a sample size greater than or equal to 30 or it is indicated that both population distributions are approximately normal. If either sample size is less than 30, both sample data distributions should be free from strong skewness and outliers.