Question

A student was asked to find a 98% confidence interval for the population proportion of students who take notes using data from a random sample of size n = 84. Which of the following is a correct interpretation of the interval 0.1 < p < 0.33?

Check all that are correct.

• ____With 98% confidence, the proportion of all students who take notes is between 0.1 and 0.33.
• ____The proprtion of all students who take notes is between 0.1 and 0.33, 98% of the time.
• ____With 98% confidence, a randomly selected student takes notes in a proportion of their classes that is between 0.1 and 0.33.
• ____There is a 98% chance that the proportion of the population is between 0.1 and 0.33.
• ____There is a 98% chance that the proportion of notetakers in a sample of 84 students will be between 0.1 and 0.33.

Answer 1

Given the 98% confidence interval for the population proportion of the students who takes notes is

0.1 < p < 0.33

Correct interpretation is

*  The proprtion of all students who take notes is between 0.1 and 0.33, 98% of the time.

*There is a 98% chance that the proportion of the population is between 0.1 and 0.33.

(Simple meaning of 98% confidence interval :

If we draw various samples of size n from the given population and we construct 98% confidence intervals using these samples , then 98% of these intervals would contain the true population parameter.)