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AP Statistics 3.10.D Standard Error for Two Proportions

Practise calculating the unpooled standard error for a difference in population proportions by using each sample proportion and sample size in its own variance term.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • Compute each sample-proportion variance separately and add the terms before taking the square root.
  • Use each group's own p-hat and sample size instead of a pooled proportion for confidence intervals.

3.10.D—Calculate the standard error and margin of error for estimating the difference between two population… question 1

[Maximum number: 1]

A polling organization surveyed 2,002 randomly selected adults who are not scientists and 3,748 randomly selected adults who are scientists. Each adult was asked the question "Do you think that genetically modified foods are safe to eat?" Of those who are not scientists, 37 percent responded yes, and of those who are scientists, 88 percent responded yes. Which of the following is the standard error used to construct a confidence interval for the difference between the proportions of all adults who are not scientists and all adults who are scientists who would answer yes to the question?

A

(0.37)(0.63)2,002+(0.88)(0.12)3,748\sqrt{\frac{(0.37)(0.63)}{2,002}+\frac{(0.88)(0.12)}{3,748}}

B

(0.37)(0.63)2,002−(0.88)(0.12)3,748\sqrt{\frac{(0.37)(0.63)}{2,002}-\frac{(0.88)(0.12)}{3,748}}

C

(0.37)(0.63)2,002+(0.88)(0.12)3,748\sqrt{\frac{(0.37)(0.63)}{2,002}}+\sqrt{\frac{(0.88)(0.12)}{3,748}}

D

(0.70)(0.30)2,002+(0.70)(0.30)3,748\sqrt{\frac{(0.70)(0.30)}{2,002}}+\sqrt{\frac{(0.70)(0.30)}{3,748}}

E

(0.37)(0.63)2,002+(0.88)(0.12)3,748\frac{(0.37)(0.63)}{\sqrt{2,002}}+\frac{(0.88)(0.12)}{\sqrt{3,748}}

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