Question

a student was asked to find a 98% confidence interval for the proportion of students who take notes using data from a random sample of size n = 79. which of the following is a correct interpretation of the interval 0.12 < p < 0.28?

there is a 98% chance that the proportion of notetakers in a sample of 79 students will be between 0.12 and 0.28.

the proportion of all students who take notes is between 0.12 and 0.28, 98% of the time.

with 98% confidence, a randomly selected student takes notes in their classes with a proportion between 0.12 and 0.28.

there is a 98% chance that the proportion of the sample is between 0.12 and 0.28.

with 98% confidence, the proportion of all students who take notes is between 0.12 and 0.28.

Explanation:

A confidence interval gives an estimate of where the population parameter (in this case, the proportion of all students who take notes) lies. A 98% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 98% of those intervals would contain the true population proportion. It is not about the sample proportion (options 1 and 4 are incorrect as they refer to the sample proportion), not about the proportion being in the interval a certain percentage of time (option 2 is incorrect), and not about a single student (option 3 is incorrect).

Answer:

With 98% confidence, the proportion of all students who take notes is between 0.12 and 0.28.