Question

Obtain a sample size that will ensure a margin of error of at most the one specified.

Margin of error$=0.02$

Confidence level$=90\%$

Short answer

The required sample size is$1692.$

Step-by-step solution

Given information

The given data is

Margin of error $=0.02$

Confidence level $=90\%$

Explanation

Margin of error$=0.02$

Confidence level $=90\%$

When the margin of error is $0.02$and the confidence level is $90\%$, calculate the sample size.

With a $90\%$confidence level, the required value of $z_{\frac{a}{2}}$from table areas under the standard normal curve is $1.645$.

The sample size is

$n=0.25{\left(\frac{z_{\frac{\alpha }{2}}}{E}\right)}^2$

$=0.25{\left(\frac{1.645}{0.02}\right)}^2$

$=0.25(6,765.0625)$

$=1,691.266$

$\approx 1692.$