A You want to estimate the proportion of vegans living in a

A.) You want to estimate the proportion of vegans living in a town. You have no prior information about this proportion and you want to estimate it with 90%confidence interval within plus and minus 0.03. What is the minimum sample size you must choose? Enter the appropriate INTEGER here.

Please repeat for a 95% confidence interval within plus and minus 0.05 and a 90% confidence interval within plus and minus 0.05.

Solution

a) at 90%confidence interval within plus and minus 0.03
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.64
Samle Proportion = 0.5
ME = 0.06
n = ( 1.64 / 0.06 )^2 * 0.5*0.5
= 186.778 ~ 187

b)
at 95%confidence interval within plus and minus 0.05
Z a/2 at 0.05 is = 1.96
Samle Proportion = 0.5
ME = 0.1
n = ( 1.96 / 0.1 )^2 * 0.5*0.5
= 96.04 ~ 97

at 90%confidence interval within plus and minus 0.05
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.64
Samle Proportion = 0.5
ME = 0.1
n = ( 1.64 / 0.1 )^2 * 0.5*0.5
= 67.24 ~ 68