Question

Linda Barnes has learned from prior studies that one out of five applicants gets admitted to top MBA programs in the country. She wishes to construct her own 95% confidence interval for the acceptance rate in top MBA programs. How large a sample should she take if she does not want the acceptance rate of the sample to deviate from that of the population by more than seven percentage points?

Answer 1

Answer: 126

Step-by-step explanation:

As per given , we have

Prior Population proportion : $p=\dfrac{1}{5}=0.2$

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

Critical value for 95% confidence interval (using the z-value table) = $z_{\alpha/2}=1.96$

Margin of error (maximum error): $E=7\%=0.07$

Formula to find the sample size :

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\ n=0.20(1-0.20)(\dfrac{1.96}{0.07})^2\\\\ n=125.44\approx126$

Therefore , the required minimum sample size = 126