Question

You wish to estimate the estimate with a 98% level of confidence the proportion of the U.S. adult population that would vote for a socialist government. Your estimate must be accurate within 2%.

Without a preliminary sample available, estimate the minimum survey sample size (n):

If a prior survey found that 43% of U.S. adults would support some sort of socialist government, determine the minimum sample size (n):

Answer 1

Solution:
Given in the question
Confidence level = 0.98
level of significance() = 1 - Confidence level = 1 - 0.98 = 0.02
/2 = 0.02/2 = 0.01
From Z table we found Z/2 = 2.32635
P(U.S. Adults would support some sort of socialist government) = 0.43
Margin of error(E) = 0.02
So sample size can be calculated as
Sample size (n) = (Z/2 / E)^2 * (p*(1-p)) = (2.32635/0.02)^2/(0.43*(1-0.43)) = 3316
So minimum sample size required (n) = 3316