Exercise · ZW-CONFIDENCE-INTERVAL-008 · ★★☆ Intermediate
With \(\sigma=10\) and \(95\,\%\) confidence (\(z=1.96\)), what is the smallest \(n\) giving a margin of error of at most \(2\)?
Choose one option.
Show answer
- D. \(97\)
Explanation
We need \(1.96\cdot10/\sqrt n\le2\), that is \(n\ge(9.8)^2=96.04\). Since \(n\) is an integer, round up: \(97\).
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-001 A sample of n=36 has bar x=50 and known σ=12. Use z=1.96. What is the 95 \% confidence interval for…
- 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?
- ZW-CONFIDENCE-INTERVAL-004 A confidence interval for μ is (12.4,\ 15.6), built symmetrically around bar x. What is bar x?
- 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-009 What does «95 \% confidence» mean?