Question

Margin of error: 0.04; confidence level: 95%; from a prior study, bold p with bold overparenthesis on top is estimated by the decimal equivalent of 89%. Find the sample size.

Answer 1

Answer: 235

Explanation:

The formula to calculate the sample size :-

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

Given : Estimated proportion
`\hat{p}=0.89`

Margin of error :
`E=0.04`

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

Critical value :
`z_(\alpha/2) =1.96`

Now, the required sample size will be :-

`n=(0.89(0.11))(((1.96))/(0.04))^2`

`\Rightarrow\ n= 235.057\approx235`

Hence, the required minimum sample size = 235