Exercise · ZW-CONFIDENCE-INTERVAL-002 · ★☆☆ Basic
With \(\sigma=10\), \(n=25\) and \(z=1.96\), what is the margin of error?
Choose one option.
Show answer
- D. \(3.92\)
Explanation
\(z\,\sigma/\sqrt n=1.96\cdot10/5=3.92\).
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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- ZW-CONFIDENCE-INTERVAL-005 For the same interval (12.4,\ 15.6), what is the margin of error?
- ZW-CONFIDENCE-INTERVAL-006 With the same data, what happens to the interval when the confidence goes from 95 \% to 99 \%?
- ZW-CONFIDENCE-INTERVAL-007 If the sample size is multiplied by 4, at the same confidence level, the margin of error…
- ZW-CONFIDENCE-INTERVAL-008 With σ=10 and 95 \% confidence (z=1.96), what is the smallest n giving a margin of error of at most…
- ZW-CONFIDENCE-INTERVAL-009 What does «95 \% confidence» mean?