Question

The professor suspects that her sample is flawed. She assigns each of the students in the class an ID number from 1 to 62 and uses Excel to select a simple random sample of ID numbers. The professor meets with the students in the sample. Each student signs a release that gives the registrar permission to use the student’s GPA to compute the sample average. The professor assures the students that the registrar will provide her with the average and not the GPAs of individual students.

The GPAs of the students in the new sample (from their academic records held by the registrar) are:

3.40

3.60

3.38

3.30

4.00

3.01

3.61

3.43

3.12

3.43

The professor uses the new sample average provided by the registrar as an estimate of the mean GPA of the students in the course. The absolute value of the error in her estimate is:

a. 0.21

b. 0.55

c. 0.01

d. 0.42

This error is -------------------- error   , and the only way to reduce its expected size is to ------------------ the sample size.

Answer 1

The sample mean = (3.40 + 3.60 + 3.38 + 3.30 +  4.00 + 3.01 +  3.61 + 3.43 + 3.12 + 3.43) / 10 =  3.43

Absolute value of the error = = =  0.55

b. 0.55

This error is sampling error   , and the only way to reduce its expected size is to increase the sample size.