An employee of the College Board analyzes the mathematics section of the SAT for 99 students and finds $ \bar{x}$ = 31.3 and s = 12.8. She reports that a 99% confidence interval for the mean number of correct answers is (27.981, 34.619). Does the interval (27.981, 34.619) cover the true mean?
Which of the following alternatives is the best answer for the above question?
A) Yes, (27.981, 34.619) covers the true mean
B) No, (27.981, 34.619) does not cover the true mean
C) We will never know whether (27.981, 34.619) covers the true mean.

Question

An employee of the College Board analyzes the mathematics section of the SAT for 99 students and finds $  \bar{x}$  = 31.3 and s = 12.8. She reports that a 99% confidence interval for the mean number of correct answers is (27.981, 34.619). Does the interval (27.981, 34.619) cover the true mean?
Which of the following alternatives is the best answer for the above question?
A) Yes, (27.981, 34.619) covers the true mean
B) No, (27.981, 34.619) does not cover the true mean
C) We will never know whether (27.981, 34.619) covers the true mean.

Quizplus · Accepted Answer

A confidence interval provides a range of values within which we expect the true mean to fall, but it does not guarantee that the true mean is within this interval. We can never be certain if the true mean is covered by a specific confidence interval.

An Employee of the College Board Analyzes the Mathematics Section xˉ \bar{x}xˉ

An Employee of the College Board Analyzes the Mathematics Section $\bar{x}$