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How can you tell a confidence-interval problem is really about a population proportion rather than a population mean?
AThe distribution is binomial, with no mean or average mentioned
BThe population standard deviation is always unknown
CThe sample size is always smaller than thirty
DThe data must come from a normal population
Answer & Solution
Correct answer: A. The distribution is binomial, with no mean or average mentioned
1. A direct test exists for recognizing a proportion problem.
2. The underlying random variable is binomial, counting successes among a fixed number of trials, with no mean or average mentioned.
3. That binomial structure is the signal to switch to the proportion formulas rather than the mean formulas.
4. Options B, C, and D describe conditions that can be true or false in either mean or proportion problems, so they do not distinguish the two.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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