Notes
See Confidence Interval Notes
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.
\(n = 59 \)
\(\,\,\,\,\,\displaystyle n=\left(\frac{z_c \sigma}{E}\right)^2\)
\(\,\,\,\,\,\displaystyle n=\left(\frac{1.96 \cdot 7.8}{2}\right)^2\)
\(\,\,\,\,\,\displaystyle n=58.4\)
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.
The sample size should be \(1068\)
\(\,\,\,\,\,\displaystyle n=\frac{1}{4}\left(\frac{z_c}{E}\right)^2\)
\(\,\,\,\,\,\displaystyle n=\frac{1}{4}\left(\frac{1.96}{.03}\right)^2\)
\(\,\,\,\,\,\displaystyle n=1067.1\)
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 \(\hat{p}=.35\)
The sample size should be \(1540\)
\(\,\,\,\,\,\displaystyle n=\left(\hat{p}\right)\left(1-\hat{p}\right)\left(\frac{z_c}{E}\right)^2\)
\(\,\,\,\,\,\displaystyle n=\left(.35\right)\left(1-.35\right)\left(\frac{1.645}{.02}\right)^2\)
\(\,\,\,\,\,\displaystyle n=1539.1\)
Round up to \(1540\)
See Related Pages\(\)
