Answer:
We would need a sample of size at least 74.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
99% confidence level
So , z is the value of Z that has a pvalue of , so .
How large of a sample size is needed to estimate it to within 0.15 of the true value with 99% confidence?
We need a sample of size at least n
n is found when
We don't know the proportion, so we estimate , which is the case for which we are going to need the largest sample size.
Rounding up
We would need a sample of size at least 74.