Question

ga political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed

Answer 1

Answer: 151

Explanation:

if prior population proportion is unknown , then the formula is used to find the sample size :

`n=0.25((z_(\alpha/2))/(E))^2`

, where
`z_(\alpha/2)` = Two tailed critical value for significance level of
`\alpha.`

E = Margin of error.

Given : margin of error = 8%= .08

For 95% confidence level , two tailed critical value = 1.96

Now, the required sample size :

`n=0.25((1.96)/(0.08))^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151`

Hence, the size of the sample needed = 151.