Question

It is believed that 40% of all voters favor a particular candidate. How large of a simple random sample is required so that the margin of error of the 95% confidence interval of all voters who favor the candidate is 3%

Answer 1

1024 samples

Explanation:

Given that:

Mean number of voters p = 40% = 0.4

Error, E= 0.03

Zcritical at 95% = 1.96

Using the relation :

n = p(1 - p) / (E / Zcritical)^2

n = 0.4(0.6) / (0.03 / 1.96)^2

n = 0.24 / 0.0002342

n = 1024.4266

n = 1024 samples