A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 2 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.

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.

the infinity sign

step-by-step explanation:

all it means is function 3