Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions? A) n₁p₁ ≥ 30 and n₂p₂ ≥ 30 B) n₁p₁ ≥ 5 and n₂p₂ ≥ 5 C) n₁p₁ ≥ 5 , n₁(1-p₁) ≥ 5 , n₂p₂ ≥ 5 and n₂(1-p₂) ≥ 5 D) n₁p̂₁ ≥ 5 , n₁(1-p̂₁) ≥ 5 , n₂p̂₂ ≥ 5 and n₂(1-p̂₂) ≥ 5 E) n₁p₁ ≥ 10 and n₂p₂ ≥ 10

Question

Quizplus · Accepted Answer

The required conditions for using the normal approximation to the binomial in testing the difference between two population proportions are that both sample sizes (n1 and n2) must be large enough such that np ≥ 5 and n(1-p) ≥ 5 for both groups (1 and 2). Therefore, the correct answer is C because it includes both requirements for both groups. Choices A and E only meet the requirement for one group, and choices B and D use the sample proportion (p̂) instead of the true population proportion (p) in the formula for the standard deviation, which is not appropriate for small sample sizes.

Which of the Following Is a Required Condition for Using