Exercise · ZW-CONFIDENCE-INTERVAL-010 · ★★★ Advanced
A \(95\,\%\) interval for \(\mu\), with \(n=16\) and known \(\sigma\), is \((4.02,\ 5.98)\). What is \(\sigma\)?
Choose one option.
Show answer
- B. \(2\)
Explanation
The margin is \((5.98-4.02)/2=0.98=1.96\,\sigma/4\), so \(\sigma=2\). The value \(0.98\) is the margin, not the standard deviation.
Review the concept: Confidence interval
A confidence interval \([L,U]\) is a range of values, computed from the sample \(X\), that contains the parameter \(\theta\) with a preset probability \(P\), the confidence level \(1-\alpha\).
\[P\big(L(X)\le\theta\le U(X)\big)=1-\alpha\]
More practice problems: confidence interval
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