You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 32%. You would like to be 90% confident that your estimate is within 4% of the true population proportion. How large of a sample size is required?

We need a sample size of at least 369.

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:

For this problem, we have that:

90% confidence level

So , z is the value of Z that has a pvalue of , so .

How large of a sample size is required?

We need a sample size of at least n.

n is found when . So

Rounding up

We need a sample size of at least 369.

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step-by-step explanation: