Exercise · ZW-CONFIDENCE-INTERVAL-001 · ★☆☆ Basic
A sample of \(n=36\) has \(\bar x=50\) and known \(\sigma=12\). Use \(z=1.96\). What is the \(95\,\%\) confidence interval for \(\mu\)?
Choose one option.
Show answer
- A. \((46.08,\ 53.92)\)
Explanation
The standard error is \(12/\sqrt{36}=2\) and the margin is \(1.96\cdot2=3.92\). Forgetting to divide by \(\sqrt n\) gives absurdly wide margins.
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
- ZW-CONFIDENCE-INTERVAL-002 With σ=10, n=25 and z=1.96, what is the margin of error?
- ZW-CONFIDENCE-INTERVAL-003 What is the critical value z for a 99 \% confidence level?
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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?