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$=95\%$

Short answer

The required sample size is$2,401.$

Step-by-step solution

Given information

The given are

Margin of error $=0.02$

Confidence level $=95\%$

Explanation

The given data is

Margin of error$=0.02$

Confidence level $=95\%$

When the margin of error is $0.02$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

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

$=0.25{\left(\frac{1.96}{0.02}\right)}^2$

$=0.25(9,604)$

$=2,401.$