Out of a sample of 94 purchases at the drive-up window of a fast-food establishment, 27 were made with a major credit card. Find a 98% confidence interval for the population proportion of purchases paid with a major credit card.

The 98% confidence interval for the population proportion of purchases paid with a major credit card is (0.1786, 0.3958).

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 .

For this problem, we have that:

98% confidence level

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

The lower limit of this interval is:

The upper limit of this interval is:

The 98% confidence interval for the population proportion of purchases paid with a major credit card is (0.1786, 0.3958).