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Among various ethnic groups, height standard deviation is about three inches. For 48 randomly surveyed male Swedes with x-bar = 71 inches, why can the normal-distribution method be used for a 95% confidence interval?
AThe population standard deviation is unknown and n is small
BThe sample was collected without any randomization
CThe confidence level chosen is below 90%
DThe population standard deviation is known and n exceeds 30
Answer & Solution
Correct answer: D. The population standard deviation is known and n exceeds 30
1. The normal-distribution method for a mean requires the population standard deviation, σ, to be known in advance.
2. Here σ = 3 inches is given directly, and the sample size n = 48 is reasonably large.
3. Both conditions support using z rather than t to build the confidence interval.
4. Option A describes the opposite situation, the one that calls for the Student's t-distribution instead.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_
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