Answer :
To be 95% confident that the true proportion is calculated to within 2%, 62 voters must be questioned.
Given,
A pollster wishes to estimate the true proportion of US. voters who oppose capital punishment.
We have to find the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%
Here,
To obtain the sample size,
n = z² pq / ME²
Where,
P is the proportion of voters
M. E is the margin of error.
q is the proportion of non-voters
z is the corresponding z score
The z score for the 95% confidence interval is 1.96.
n = 1.96² pq / 0.05²
n = 1536.64 pq
If 0.2 is the proportion of voters, then 0.2 is the fraction of non-voters.
n = 1536.64 pq = 61.42
≈ 62 voters
Therefore,
62 voters can be surveyed in order to be 95% confident that the true proportion is estimated to within 2%
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