Question

Select the correct answer.
In an experiment using 30 mice, the sample proportion of the mice that gained weight after a drug injection is 0.65. What is the 99.7% confidence interval for the actual proportion in the population?

A.
between 0.602 and 0.697

B.
between 0.563 and 0.737

C.
between 0.476 and 0.824

D.
between 0.389 and 0.911

Answer 1

Use the normal-approximation 2-sided CI: p̂ ± z*sqrt[p̂(1−p̂)/n]. For 99.7% use z ≈ 3.

SE = sqrt(0.65·0.35/30) = 0.08708. Margin = 3·0.08708 = 0.2612.

CI = 0.65 ± 0.2612 = (0.389, 0.911). Answer: D.