Question

Obtain a sample size

Margin of error $=0.02$

Confidence level $=95\%$

Likely range $0.4-0.7$

Short answer

The required sample size is$2,401.$

Step-by-step solution

Given information

Obtain a sample size

Margin of error $0.02$

Confidence level $=95\%$

Likely range $0.4-0.7$

Explanation

From the given values

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 $1.96$

Use$p_g^{\text{'}}=0.5$because the value in the range closet to$0.5.$

The sample size is

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

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

$=0.25(9,604)$

$=2,401.$