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A condition governs when a normal-based confidence interval for a proportion is valid. What must be true of np' and nq'?
ABoth must be smaller than five
BTheir sum must equal exactly one
CBoth must be larger than five
Dnp' must exceed n while nq' nears zero
Answer & Solution
Correct answer: C. Both must be larger than five
1. The proportion confidence interval relies on the normal approximation to the binomial distribution.
2. That approximation is only trustworthy when both the expected successes, np', and expected failures, nq', are large enough.
3. The stated threshold is that both np' and nq' must exceed five.
4. Option B misstates a probability-sum rule that has nothing to do with this validity condition.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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