Margin of Error

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Notes

Notes for Margin of Error

Notes for Margin of Error Proportions

Notes for Margin of Error with Confidence Intervals

Notes for the Concept of Confidence Interval
See Confidence Interval Notes

Level of Confidence Chart

Notes for Finding n to Estimate a Mean

Notes for Finding n to Estimate a Proportion

Notes for Finding n Conservatively

Effects on Margin of Error

If confidence level increases, the margin of error increases.

If sample size increases, the margin of error decreases.

Practice Problems

\(\textbf{1)}\) Find \(n\) if \( \sigma =7.8\) and error is \(2\) with \(95\%\) confidence interval.
Show Answer
\(n = 59 \)
Show Work

\(\,\,\,\,\,\displaystyle n=\left(\frac{z_c \sigma}{E}\right)^2\)

\(\,\,\,\,\,\displaystyle n=\left(\frac{1.96 \cdot 7.8}{2}\right)^2\)

\(\,\,\,\,\,\displaystyle n=58.4\)

Round up to \(59\)

\(\textbf{2)}\) How large should the sample be if you want to do a \(90\%\) confidence level and error is .03 from p and there is no preliminary study.
Show Answer
The sample size should be \(1068\)
Show Work

\(\,\,\,\,\,\displaystyle n=\frac{1}{4}\left(\frac{z_c}{E}\right)^2\)

\(\,\,\,\,\,\displaystyle n=\frac{1}{4}\left(\frac{1.96}{.03}\right)^2\)

\(\,\,\,\,\,\displaystyle n=1067.1\)

Round up to \(1068\)

\(\textbf{3)}\) How large should the sample be if you want to do an \(90\%\) confidence level and width of interval was \(.04\) and prelim study found that \(\hat{p}=.35\)
Show Answer
The sample size should be \(1540\)
Show Work

\(\,\,\,\,\,\displaystyle n=\left(\hat{p}\right)\left(1-\hat{p}\right)\left(\frac{z_c}{E}\right)^2\)

\(\,\,\,\,\,\displaystyle n=\left(.35\right)\left(1-.35\right)\left(\frac{1.645}{.02}\right)^2\)

\(\,\,\,\,\,\displaystyle n=1539.1\)

Round up to \(1540\)

See Related Pages\(\)

\(\bullet\text{ Statistics Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Margin of Error}\)
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\(\bullet\text{ Confidence Intervals}\)
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\(\bullet\text{ Standard Error}\)
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\(\bullet\text{ Confidence Level}\)
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\(\bullet\text{ Type I and Type II Errors}\)
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\(\bullet\text{ One Sample z-test}\)
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\(\bullet\text{ Two Sample z-test for Difference Between Means}\)
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\(\bullet\text{ Hypothesis Test- Difference Between Proportions}\)
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\(\bullet\text{ Chi-squared test}\)
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