A researcher calculates the 95% confidence interval for a mean as 48.2 to 55.8. A second study using the same sample size finds a 99% confidence interval for the same parameter. Which of the following correctly describes the expected change?

• A The interval narrows because higher confidence requires more precision
• B The interval remains the same because sample size is unchanged
• C The interval widens only if the standard deviation increases
• D The interval widens because a higher z-value is used ✓

Explanation

Confidence interval width = 2 × z × (SD/√n). For 95% CI, z = 1.96; for 99% CI, z = 2.58. Since n and SD are unchanged but z increases, the interval widens. Wider intervals reflect greater certainty of capturing the true parameter at the cost of reduced precision.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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