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The population standard deviation for the age of Foothill College students is 15 years. To be 95% confident the sample mean age is within EBM=2 years of the true mean, the sample-size formula n = z^2*σ^2/EBM^2 gives n ≈ 216.09. Why should 217 students be surveyed, not 216?
ARound down, since 216 students already exceed the target
BAlways round the sample size up to the next higher integer
CAdd exactly one student as a safety margin, always
D217 is simply an unrelated typographical error
Answer & Solution
Correct answer: B. Always round the sample size up to the next higher integer
1. The sample-size formula gives a fractional value of 216.09 students, which is not a whole person.
2. Because 216 students would fall just short of the required precision, the standard rule is to always round up.
3. Rounding 216.09 up gives 217 students, guaranteeing the sample is at least large enough.
4. Option A would leave the sample slightly too small to guarantee the desired error bound, so it is not used.
_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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