At the movies: A movie theater is considering a showing of The Princess Bride for a 80's thowback night. In order to ensure the success of the evening, they've asked a random sample of 53 patrons whether they would come to the showing or not. Of the 53 patrons, 18 said that they would come to see the film. Construct a 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing.

The 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing is (0.2121, 0.4671).

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 z-score that has a p-value of .

Of the 53 patrons, 18 said that they would come to see the film.

This means that

95% confidence level

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

The lower limit of this interval is:

The upper limit of this interval is:

The 95% confidence interval to determine the true proportion of all patrons who would be interested in attending the showing is (0.2121, 0.4671).

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step-by-step explanation: