A professor was curious about her students' grade point averages (GPAs). She took a random Sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of The following formulas gives a 99% confidence interval for the mean GPA of the professor's Students?
A) $3.01 \pm 2.977 ( 0.534 / \sqrt { 15 } )$
B) $3.01 \pm 2.977 ( 0.534 / \sqrt { 14 } )$
C) $3.01 \pm 2.576 ( 0.534 / \sqrt { 15 } )$
D) $3.01 \pm 2.947 ( 0.534 / \sqrt { 15 } )$
E) $3.01 \pm 2.947 ( 0.534 / \sqrt { 14 } )$

Question

A professor was curious about her students' grade point averages (GPAs). She took a random Sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of The following formulas gives a 99% confidence interval for the mean GPA of the professor's Students? 
A) $3.01 \pm 2.977 ( 0.534 / \sqrt { 15 } )$
B) $3.01 \pm 2.977 ( 0.534 / \sqrt { 14 } )$
C) $3.01 \pm 2.576 ( 0.534 / \sqrt { 15 } )$
D) $3.01 \pm 2.947 ( 0.534 / \sqrt { 15 } )$
E) $3.01 \pm 2.947 ( 0.534 / \sqrt { 14 } )$

Quizplus · Accepted Answer

For a 99% confidence interval with a sample size of 15, the t-distribution critical value is approximately 2.977. The formula uses the sample standard deviation divided by the square root of the sample size (15).

A Professor Was Curious About Her Students' Grade Point Averages 3.01±2.977(0.534/15)3.01 \pm 2.977 ( 0.534 / \sqrt { 15 } )3.01±2.977(0.534/15​)

A Professor Was Curious About Her Students' Grade Point Averages $3.01 \pm 2.977 ( 0.534 / \sqrt { 15 } )$