After receiving several complaints from his customers about the store being closed on Sundays, a storekeeper decided to conduct a survey. He randomly selected 100 female customers and 120 male customers and asked them, "Are you interested in shopping at this store on Sundays?" He counted the number of customers answering "yes" and constructed a 95 percent confidence interval for the difference by subtracting the proportion of female customers from the proportion of male customers in favor of shopping on Sundays. The resulting interval was $$$(-0.23,-0.18)$$$. Which of the following is a correct interpretation of the interval?

We are 95 percent confident that the proportion of females interested in shopping on Sundays exceeds the proportion of males interested in shopping on Sundays.

We are 95 percent confident that the proportion of males interested in shopping on Sundays exceeds the proportion of females interested in shopping on Sundays.

We are 95 percent confident that the proportion of females interested in shopping on Sundays is equal to the proportion of males interested in shopping on Sundays.

Because the interval contains negative values, the interval is invalid and should not be interpreted.

Because the interval does not contain zero, the interval is invalid and should not be interpreted.

Statistics

College Board

Exam No：AP Statistics Problem Set 10 Year：2024 Question No：36

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6.8 Confidence Intervals for the Difference of Two Proportions

6.9 Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions

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