Answer: a) 8359 b) 384
Step-by-step explanation:
Given : Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}}=\pm1.96[/tex]
Margin of error : [tex]E=0.01[/tex]
a) If previous estimate of proportion : [tex]p=0.32[/tex]
Formula to calculate the sample size needed for interval estimate of population proportion :-
[tex]n=p(1-p)(\frac{z_{\alpha/2}}{E})^2[/tex]
[tex]\Rightarrow\ n=0.32(1-0.32)(\frac{1.96}{0.01})^2=8359.3216\approx 8359[/tex]
Hence, the required sample size would be 8359 .
b) If she does not use any prior estimate , then the formula to calculate sample size will be :-
[tex]n=0.25\times(\frac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=0.25\times(\frac{1.96}{0.05})^2=384.16\approx384[/tex]
Hence, the required sample size would be 384 .
