A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.05 with 95% confidence if (a) she uses a previous estimate of 0.32? (b) she does not use any prior estimates?
Accepted Solution
A:
Answer: a) 8359 b) 384Step-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 .