Standard Error for Difference in Proportions
A study compared the proportion of adults who exercise regularly in two cities. In a random sample of 300 adults from City A, 120 reported exercising regularly. In an independent random sample of 400 adults from City B, 150 reported exercising regularly. Which formula should be used to calculate the standard error for a confidence interval for the difference in the population proportions?
A
√[(p̂₁-p̂₂)(1-(p̂₁-p̂₂))/n₁n₂]
B
√[p̂₁(1-p̂₁)/n₁ - p̂₂(1-p̂₂)/n₂]
C
√[p̂(1-p̂)(1/n₁ + 1/n₂)]
D
√[p̂₁(1-p̂₁)/n₁ + p̂₂(1-p̂₂)/n₂]
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