4
QuizMultiple Choice

Estimating a Population Proportion

Question 4 • CA-Statistics and Probability B

A random sample of adults was surveyed about their exercise habits. Of the 100 surveyed, 56 stated they exercise regularly. Which of the following is the 95% confidence interval for p, the proportion of all adults who exercise regularly?Find the z-table here.

Answer
A
(0.50, 0.62)
B
(0.48, 0.64)
C
(0.46, 0.66)
D
(0.43, 0.69)

Explanation

The sample proportion is 56/100 = 0.56. Its standard error is √(0.56 × 0.44 / 100) ≈ 0.050, so a 95% confidence interval is 0.56 ± 1.96(0.050), or approximately (0.46, 0.66). Therefore, the correct choice is C, (0.46, 0.66).

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