In a study of typical student grade-point averages (GPAs), we sample 16 students and find an average GPA of 2.76, with a standard deviation of 0.48.Assuming the GPAs are normally distributed, what is an interval that we can be 80% certain contains the mean student GPA?
A) (2.12, 3.40)
B) (2.61, 2.91)
C) (2.60, 2.92)
D) (2.66, 2.86)

Question

Quizplus · Accepted Answer

We can use a t-distribution with 15 degrees of freedom (n-1) to find the interval. From the t-distribution table (or using a calculator), we find the t-score that corresponds to 80% confidence with 15 degrees of freedom to be approximately 1.341.

The margin of error is calculated as:

margin of error = t-score * standard error

where the standard error is the standard deviation divided by the square root of the sample size:

standard error = 0.48 / sqrt(16) = 0.12

Thus, the margin of error is:

margin of error = 1.341 * 0.12 = 0.16

To find the interval, we take the sample mean and add/subtract the margin of error:

interval = sample mean +/- margin of error

interval = 2.76 +/- 0.16

interval = (2.60, 2.92)

Therefore, the answer is choice C, (2.60, 2.92), which is the interval we can be 80% certain contains the mean student GPA.

In a Study of Typical Student Grade-Point Averages (GPAs), We