Question

Obtain a sample size

Margin of error $=0.01$

Confidence level $=95\%$

likely range$=0.2-0.4$

Short answer

The required sample size is$9,604.$

Step-by-step solution

Given information

Margin of error $=0.01$

Confidence level $=95\%$

Likely range $0.2-0.4$

Explanation

From the given data

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 $1.96$

Use $p_g^{\text{'}}=0.4$because the value in the range closet to $0.5$

The sample size is

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

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

$=0.25(38,416)$

$=9,604.$