City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. They take a sample of 400 visitors and find that 100 are on a second visit. The 99% confidence interval is 0.1942 to 0.3058. The correct interpretation of the interval is
A) We are 99% confident that between 19.42% and 30.58% of visitors are on a second visit.
B) The proportion of repeat visitors is between 19.42% and 30.58%.
C) The probability is 95% that between 19.42% and 30.58% of visitors are on a second visit.
D) The margin of error is between 19.42% and 30.58%.
E) All samples of 400 will have between 19.42% and 30.58% of visitors on a second visit.

Question

Quizplus · Accepted Answer

The correct interpretation of the 99% confidence interval is that we are 99% confident that the true proportion of visitors who are repeat visitors falls between 19.42% and 30.58%. Therefore, choice A is the best choice because it accurately reflects the meaning of a confidence interval. Choice B is too definitive because it does not reflect the uncertainty inherent in a confidence interval. Choice C is incorrect because confidence intervals do not provide information about probability. Choice D is incorrect because it does not accurately reflect the meaning of a confidence interval. Choice E is incorrect because it assumes that the sample is representative of the population, which may not be the case.

City Officials Want to Estimate the Proportion of Visitors Who