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

Step-by-step explanation:

The formula to calculate the sample size  :-

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

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 :-

$n=(0.89(0.11))(\dfrac{(1.96)}{0.04})^2$

$\Rightarrow\ n= 235.057\approx235$

Hence, the required minimum sample size = 235