Answer:
She needs a sample of at least 385.
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:
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
How large a sample should she take to achieve this?
She needs a sample of size at least n.
n is found when M = 0.04.
We do not know the true population proportion, so we use , which is the case for which we are going to need the largest sample size.
Dividing both sides by 0.05
Rounding up
She needs a sample of at least 385.