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Starting from the exam-score example with n=36 and EBM=0.8225 at 90% confidence, what happens to the error bound if the sample size is increased to n=100, holding σ and the confidence level fixed?
AThe error bound increases, to about 1.6450
BThe error bound stays exactly the same
CThe error bound decreases to exactly zero
DThe error bound decreases, to about 0.4935
Answer & Solution
Correct answer: D. The error bound decreases, to about 0.4935
1. EBM = z(σ/sqrt(n)), so a larger n makes the denominator sqrt(n) larger.
2. With n=100: EBM = (1.645)(3/sqrt(100)) = (1.645)(0.3) ≈ 0.4935.
3. This is smaller than the original EBM of 0.8225 at n=36.
4. Option C is impossible, since a positive sample standard deviation always leaves some nonzero error bound.
_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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