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) $3.01 \pm 2.576 ( 0.534 / \sqrt { 15 } )$
C) $3.01 \pm 2.977 ( 0.534 / \sqrt { 14 } )$
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) $3.01 \pm 2.576 ( 0.534 / \sqrt { 15 } )$
C) $3.01 \pm 2.977 ( 0.534 / \sqrt { 14 } )$
D) $3.01 \pm 2.947 ( 0.534 / \sqrt { 15 } )$
E) $3.01 \pm 2.947 ( 0.534 / \sqrt { 14 } )$

Quizplus · Accepted Answer

The correct formula for a 99% confidence interval for the mean GPA is:$ \mu \pm z_{\alpha/2} ( \sigma / \sqrt { n } ) $where:$\mu$ is the population mean$z_{\alpha/2}$ is the z-score corresponding to the desired confidence level$\sigma$ is the population standard deviation$n$ is the sample sizeIn this case, we have:$\mu = 3.01$$z_{\alpha/2} = 2.977$ (for a 99% confidence level)$\sigma = 0.534$$n = 15$Plugging these values into the formula, we get:$3.01 \pm 2.977 ( 0.534 / \sqrt { 15 } )$Therefore, the correct answer is A.

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 $3.01 \pm 2.977 ( 0.534 / \sqrt { 15 } )$