Question

Campus athletics is interested in the proportion of registered students living on campus who play basketball recreationally during the semester. They take a random sample of 222 registered students listed as living in campus housing and ask each whether or not they do so. A 95% confidence interval is correctly calculated from this data as (0.12, 0.18). Which of the following is the correct interpretation of this confidence interval?

a. None of these are correct.
b. We are 95% contident that the proportion of the 111 sampled students that actually play basketball is between 0.12 and 0.18
c. The sample proportion of on-campus students that play basketball will be between 0.12 and 0.18 in 95% of samples of size 111
d. We are 95% confident that the proportion of all students that live on campus who play basketball recreationally is between 0.12 and 0.18
e. We are 95% confident that among the population of students that play basketball recreationally, the proportion who live on campus is between 0.12 and 0.18

Answer 1

d. We are 95% confident that the proportion of all students that live on campus who play basketball recreationally is between 0.12 and 0.18

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

A 95% confidence interval is correctly calculated from this data as (0.12, 0.18).

So the correct interpretation is that we are 95% sure that the population mean is in this interval, and the correct answer is given by option d.