Question

A researcher wants to estimate the percent of the population that uses the radio to stay informed on local news issues. The researcher wants to estimate the population proportion with a 95% level of confidence. He estimates from previous studies that no more than 30% of the population stay informed on local issues through the radio. The researcher wants the estimate to have an error of no more than .03. The necessary sample size is at least _______.

Answer 1

Answer: 896

Step-by-step explanation:

Given The prior estimate of proportion of the population stay informed on local issues through the radio: $p=0.3$

Margin of error : $E=0.03$

Significance level : $\alpha: 1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

The formula to find the sample size :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\ n=(0.3)(0.7)(\dfrac{1.96}{0.03})^2=896.373333333\approx896$

Hence, the necessary sample size is at least 896 .