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The same exam-score data (σ=3, n=36, x-bar=68) gives a 90% CI of (67.18, 68.82). Raising the confidence level to 95% gives z(0.025)=1.96, EBM=0.98, and a new CI of (67.02, 68.98). What general rule does this illustrate?
AIncreasing the confidence level narrows the confidence interval
BThe confidence level has no effect on interval width
CIncreasing the confidence level widens the confidence interval
DA higher confidence level always shifts x-bar itself
Answer & Solution
Correct answer: C. Increasing the confidence level widens the confidence interval
1. Compare the two intervals: the 90% CI spans 67.18 to 68.82, and the 95% CI spans 67.02 to 68.98.
2. The 95% interval is wider than the 90% interval.
3. This matches the general rule that raising the confidence level increases the error bound and widens the interval.
4. Option A states the opposite of what actually happened between these two computed intervals.
_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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