Question

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of​ error: nine percentage​ points; confidence level 95​%; from a prior​ study, p with caret is estimated by the decimal equivalent of 38​%.

Answer 1

Answer: 112

Step-by-step explanation:

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

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

Margin of error : E = 9%=0.09

The estimated proportion of caret : p =0.38

Now, the formula to find the sample size :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

i.e. $n=(0.38)(1-0.38)(\dfrac{1.96}{0.09})^2$

$=111.738390123\approx112$

Hence, the required minimum sample size = 112