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AP Statistics 3.10.B Conditions for Two-Proportion Intervals

Practise checking whether two-proportion interval conditions are met, especially whether the compared proportions come from genuinely independent samples or groups.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • Verify that the two proportions come from independent groups before using a two-sample z-interval.
  • Do not treat two response categories measured on the same sampled people as independent samples.

3.10.B—Justify the appropriateness of constructing a confidence interval for the difference between two population… question 1

[Maximum number: 1]

35. In a random sample of 1,500 college students, a pollster found 45\% prefer a female president and 42%42 \% prefer a male president. To calculate a 95 percent confidence interval for the difference in the proportion of college students who prefer a female president over a male president, he uses (0.45−0.42)±1.96(0.45)(0.55)1,500+(0.42)(0.58)1,500(0.45-0.42) \pm 1.96 \sqrt{\frac{(0.45)(0.55)}{1,500}+\frac{(0.42)(0.58)}{1,500}}. Were conditions for inference met?

A

Yes, because there was a random sample, 1,500 is less than 10\% of all college students, and 1,500(0.45), 1,500(0.55), 1,500(0.42), and 1,500(0.58) are all ≥10\geq 10.

B

No, because there was no random assignment between female and male college students.

C

No, because the independence assumption is violated.

D

No, because the random sample may not be truly representative of the population.

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