I want to take a survey of students at my university to find out what proportion like the new bus service on campus. I believe that 75% of students like the service. How many students will I need to survey if I want to estimate, with 99% confidence, the true proportion to within 2%?

You will need to sample at least 3108 students.

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 .

In this problem, we have that:

99% confidence level

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

The margin of error is:

How many students will I need to survey if I want to estimate, with 99% confidence, the true proportion to within 2%?

You need a sample size of at least n.

n is found when M = 0.02. So

You will need to sample at least 3108 students.

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