Answer:
A sample of 16577 is required.
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 z-score that has a p-value of .
The margin of error is of:
99% confidence level
So , z is the value of Z that has a p-value of
, so
.
She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?
We have no estimation for the proportion, and thus we use , which is when the largest sample size will be needed.
The sample size is n for which M = 0.01. So
Rounding up:
A sample of 16577 is required.