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Problem-Solving and Data AnalysisHardConfidence level and interval width

Problem-Solving and Data Analysis practice question

From one random sample, a researcher computes two intervals for a population mean: one at a 90% confidence level and one at a 99% confidence level. Which statement is true?

  1. A. The 99% interval is wider, because greater confidence requires allowing a larger margin around the estimate.Correct
  2. B. The 90% interval is wider, because a lower confidence level is less precise.
  3. C. The two intervals are the same width, because they come from the same sample.
  4. D. The 99% interval is narrower, because it is more accurate.

Answer: A. The 99% interval is wider, because greater confidence requires allowing a larger margin around the estimate.

To be more confident of capturing the true mean, the interval must cover more ground. Same sample, higher confidence, wider interval.

Why the other answers are wrong

B. The 90% interval is wider, because a lower confidence level is less precise.
Lower confidence lets the interval be NARROWER — you accept more risk of missing the true value.
C. The two intervals are the same width, because they come from the same sample.
The sample fixes the estimate and its standard error, but the confidence level scales the margin: 99% uses a bigger multiplier.
D. The 99% interval is narrower, because it is more accurate.
'More accurate' isn't what confidence means; a 99% interval is more likely to contain the truth precisely because it is wider.

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