6
QuizMultiple Choice

Estimating a Population Proportion

Question 6 • CA-Statistics and Probability B

A recent study estimated that 68% of US adults enjoy reading a book while relaxing. How many adults are required for a random sample to obtain a margin of error of at most 0.05 with 90% confidence?Find the z-table here.

Answer
A
236
B
271
C
335
D
578

Explanation

For a proportion, use n = z²p(1 − p)/E². At 90% confidence, z ≈ 1.645; with p = 0.68 and margin of error E = 0.05, n = (1.645)²(0.68)(0.32)/(0.05)² ≈ 235.5. Round up to ensure the margin of error is at most 0.05, so the required sample is 236 adults, choice A.

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