A city library selects a random sample of 1,250 of its patrons and finds that the 95% confidence interval for the proportion of those who have read an e-book in the previous 12 months is (0.71, 0.75).Interpret the confidence interval.
Answer
A
We are 95% confident that the interval from 0.71 to 0.75 captures the true proportion of library patrons who have read an e-book in the previous 12 months.
B
We are 95% confident that more than half of the library’s patrons have read an e-book in the previous 12 months.
C
95% of the time between 71% and 75% of library patrons have read an e-book in the previous 12 months.
D
The library can be 95% confident that its patrons would be in favor of it offering e-books.
Explanation
A 95% confidence interval estimates the true population proportion, which is the proportion of all library patrons who read an e-book in the past 12 months. The correct interpretation is that we are 95% confident this true proportion lies between 0.71 and 0.75, or 71% and 75%. Choice B makes a narrower claim that does not express what a confidence interval means, while C incorrectly describes the proportion as varying 95% of the time.
AI-written and checked against the verified answer.