Find Sample Size

Notes

Notes for Sample Size 1

Notes for Sample Size 2

Notes for Sample Size 3

Notes for Level of Confidence

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 \(1540\)

\(\textbf{4)}\) Find \(n\) if \( \sigma =3\) and error is \(.2\) with \(99\%\) confidence interval.
Show Answer
\(n = 1492 \)
Show Work

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

\(\,\,\,\,\,\displaystyle n=\left(\frac{2.575 \cdot 3}{.2}\right)^2\)

\(\,\,\,\,\,\displaystyle n=1491.9\)

Round up to \(1492\)

\(\textbf{5)}\) How large should the sample be if you want to do a \(80\%\) confidence level and error is .02 from p and there is no preliminary study.
Show Answer
The sample size should be \(1024\)
Show Work

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

\(\,\,\,\,\,\displaystyle n=\frac{1}{4}\left(\frac{1.28}{.02}\right)^2\)

\(\,\,\,\,\,\displaystyle n=1024\)

\(\textbf{6)}\) How large should the sample be if you want to do an \(95\%\) confidence level and width of interval was \(.16\) and prelim study found that \(\hat{p}=.4\)
Show Answer
The sample size should be \(145\)
Show Work

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

\(\,\,\,\,\,\displaystyle n=\left(.4\right)\left(1-.4\right)\left(\frac{1.96}{.08}\right)^2\)

\(\,\,\,\,\,\displaystyle n=144.06\)

Round up to \(145\)

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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