Answer:
The sample size suggested by this statement is of at least 4145.
Step-by-step explanation:
This statement states that the 99% confidence interval has a margin of error of 2 percentage points.
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
.
Find the sample size suggested by this statement.
The sample size is at least n.
n is found when M = 0.02.
We don't know the true proportion, so we use , which is when the largest sample size will be needed.
Rounding up
The sample size suggested by this statement is of at least 4145.