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As the degrees of freedom of a Student's t-distribution increase, what happens to its shape?
AIts tails grow even heavier as it flattens further
BIt comes to resemble the standard normal distribution
CIts mean shifts steadily away from zero
DIt becomes skewed rather than staying symmetric
Answer & Solution
Correct answer: B. It comes to resemble the standard normal distribution
1. Every sample size produces a slightly different member of the t-distribution family.
2. As degrees of freedom grow larger, the t-distribution's extra tail weight and flatness shrink.
3. In the limit, the t-distribution's graph converges toward the graph of the standard normal distribution.
4. Option A describes the opposite trend, and options C and D contradict the t-distribution's fixed mean of zero and its symmetry.
_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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