Q:

An epidemiologist wants to estimate the proportion of residents in her city that carry the Hepatitis A virus. It is thought that the proportion is approximately 46%. How large a sample of residents should be taken to estimate the proportion who carry the Hepatitis A virus to within 8 percentage points with 95% confidence?

Accepted Solution

A:
Answer: 149Step-by-step explanation:Given :  The proportion of of residents in her city that carry the Hepatitis A virus =0.46Margin of error : [tex]E=0.08[/tex]Significance level : [tex]\alpha=1-0.95=0.05[/tex]Critical value : [tex]z_{\alpha/2} =1.96[/tex]The formula to calculate the sample size :-[tex]n=(p(1-p))(\dfrac{z_{\alpha/2}}{E})^2[/tex][tex]\Rightarrow\ n= (0.46(0.54))(\dfrac{(1.96)}{0.08})^2\\\\\Rightarrow\ n=149.1021\approx149[/tex]Hence, the required minimum sample size = 149