Question

A student was asked to find a 90% confidence interval for the proportion of students who take notes using data from a random sample of size n = 88. Which of the following is a correct interpretation of the interval 0.1 < p < 0.3?

Check all that are correct.

• The proprtion of all students who take notes is between 0.1 and 0.3, 90% of the time.
• There is a 90% chance that the proportion of notetakers in a sample of 88 students will be between 0.1 and 0.3.
• With 90% confidence, a randomly selected student takes notes in a proportion of their classes that is between 0.1 and 0.3.
• With 90% confidence, the proportion of all students who take notes is between 0.1 and 0.3.
• There is a 90% chance that the proportion of the population is between 0.1 and 0.3.

Answer 1

If (1-)100% confidence interval for population proportion is (a,b), then the interpretation of this is we can be (1-)100% confident that the population proportion lies in the interval (a,b). Here in this context, With 90% confidence, the proportion of students who takes notes is contained in the interval (0.1,0.3).

Therefore the answer is 1 and 4.

Note that confidence interval is not a probability so we cannot determine the chance using this.