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 = 78. Which of the following is a correct interpretation of the interval 0.13 < p < 0.27?

Check all that are correct.

0 There is a 90% chance that the proportion of the population is between 0.13 and 0.27.

0 The proprtion of all students who take notes is between 0.13 and 0.27, 90% of the time.

0 With 90% confidence, a randomly selected student takes notes in a proportion of their classes that is between 0.13 and 0.27.

0 With 90% confidence, the proportion of all students who take notes is between 0.13 and 0.27.

0 There is a 90% chance that the proportion of notetakers in a sample of 78 students will be between 0.13 and 0.27.

Answer 1

Correct Answers:

The proportion of all students who take notes is between 0.13 and 0.27, 90% of the time.

With 90% confidence, the proportion of all students who take notes is between 0.13 and 0.27.

Explanation:

The 90% confidence interval for the population proportion is given as (0.13, 0.27). This means, we are 90% confident that the population proportion of all students who take notes is lies between 0.13 and 0.27. In other words, 90% of the times, the population proportion of all students who take notes is lies between 0.13 and 0.27.

This is a confidence interval for population proportion and not for sample proportion. So, this confidence interval does not imply the bounds for sample of 78 students. Also, confidence interval never implies its relationship with individual observation. So, we can’t infer about a randomly selected student who take notes.