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Older statistical practice used the normal approximation for large samples and the Student's t-distribution only for samples of at most 30. What does modern practice, with graphing calculators and computers, now use instead?
AThe normal distribution for every sample, regardless of size
BThe t-distribution only for samples smaller than 10
CThe t-distribution whenever s is used as an estimate for σ
DWhichever distribution gives the narrower confidence interval
Answer & Solution
Correct answer: C. The t-distribution whenever s is used as an estimate for σ
1. Historically, statisticians switched between normal and t-distribution methods based on a sample-size cutoff of 30.
2. With modern computing power, that cutoff is no longer necessary.
3. Current practice is to use the t-distribution any time the sample standard deviation s stands in for an unknown σ, regardless of n.
4. Option D describes cherry-picking a method by interval width, which is never recommended.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.2 A Single Population Mean using the Student t Distribution_
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