Answer:
The sample size required is of 2305.
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:
A preliminary survey of adult Americans has estimated this proportion to be somewhere around 0.40.
This means that
95% confidence level
So , z is the value of Z that has a pvalue of , so .
The sample size required to estimate this proportion with 95% confidence and a margin of error of 0.02.
The sample size required is of n.
n is found when M = 0.02. So
Rounding up
The sample size required is of 2305.