Question

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

Margin of error$=0.01$

Confidence level$=95\%$

Short answer

The required sample size is$9,604.$

Step-by-step solution

Given information

The given

Margin of error $=0.01$

Confidence level $=95\%$

Explanation

Margin of error $=0.01$

Confidence level $=95\%$

When the margin of error is $0.01$and the confidence level is $95\%$, calculate the sample size.

With a $95\%$confidence level, the required value of $z_{\frac{a}{2}}$from table areas under the standard normal curve is $1.96$.

The sample size is

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

$=0.25{\left(\frac{1.96}{0.01}\right)}^2$

$=0.25(38,416)$

$=9,604.$