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

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)((z_(\alpha/2))/(E))^2`

i.e.
`n=(0.38)(1-0.38)((1.96)/(0.09))^2`

`=111.738390123\approx112`

Hence, the required minimum sample size = 112