APFIVE Standard Error for Difference in Proportions
A researcher wants to compare the proportion of adults who exercise regularly in two different cities. In City A, 120 out of 300 randomly selected adults reported exercising regularly. In City B, 150 out of 400 randomly selected adults reported exercising regularly. Which of the following is the correct formula for calculating the standard error for a confidence interval for the difference in population proportions?
A
√[p̂(1-p̂)(1/n₁ + 1/n₂)]
B
√[p̂₁(1-p̂₁)/n₁ - p̂₂(1-p̂₂)/n₂]
C
√[(p̂₁-p̂₂)(1-(p̂₁-p̂₂))/n₁n₂]
D
√[p̂₁(1-p̂₁)/n₁ + p̂₂(1-p̂₂)/n₂]
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