Answer: 235
Step-by-step explanation:
The formula to calculate the sample size :-
[tex]n=(\hat{p}(1-\hat{p}))(\dfrac{z_{\alpha/2}}{E})^2[/tex]
Given : Estimated proportion [tex]\hat{p}=0.89[/tex]
Margin of error : [tex]E=0.04[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2} =1.96[/tex]
Now, the required sample size will be :-
[tex]n=(0.89(0.11))(\dfrac{(1.96)}{0.04})^2[/tex]
[tex]\Rightarrow\ n= 235.057\approx235[/tex]
Hence, the required minimum sample size = 235
