Question

Listed in the accompanying data table are student evaluation ratings of courses and​ professors, where a rating of 5 is for​ "excellent." Assume that each sample is a simple random sample obtained from a population with a normal distribution.

a. Use the 93 course evaluations to construct a 98​% confidence interval estimate of the standard deviation of the population from which the sample was obtained.

b. Repeat part​ (a) using the 93 professor evaluations.

c. Compare the results from part​ (a) and part​ (b).

Course Eval   Prof Eval
4.0   4.6
4.4   4.6
3.5   4.1
4.3   4.7
4.5   4.5
4.4   4.4
4.3   4.1
3.4   3.3
4.8   4.9
3.9   4.0
3.1   3.3
4.0   4.1
3.6   4.3
3.5   3.5
2.7   3.1
4.4   4.8
4.1   4.7
3.6   4.0
4.3   4.9
3.7   3.2
3.1   3.5
3.4   3.5
4.3   4.2
4.6   4.4
3.8   4.1
4.5   4.8
4.2   4.4
3.8   4.2
3.6   3.7
4.3   4.8
2.2   2.4
3.2   4.5
4.4   4.7
3.8   4.4
4.0   4.5
4.3   4.3
3.7   4.1
4.1   4.1
4.0   3.8
4.4   4.6
3.3   3.5
4.7   4.7
3.2   3.4
3.6   4.1
4.4   4.3
4.6   4.6
3.6   4.0
3.4   3.9
3.8   4.3
4.4   4.5
4.3   4.2
4.3   4.0
4.4   4.7
3.6   3.9
2.9   3.5
3.8   4.1
3.7   4.0
3.7   4.4
3.5   3.7
2.9   3.3
3.8   4.2
4.3   4.5
3.6   3.8
3.1   3.5
4.2   4.6
3.4   3.6
4.0   4.4
1.9   2.5
3.2   2.8
4.2   4.5
3.3   3.8
4.5   4.5
3.5   4.3
3.9   4.0
3.5   3.9
4.6   4.2
4.2   4.6
4.5   4.3
4.0   3.8
4.6   5.2
3.6   3.4
3.6   3.2
3.6   3.9
4.5   4.5
4.7   4.8
4.2   4.5
3.4   3.3
3.3   3.2
3.7   3.9
4.3   4.1
4.0   3.5
4.2   4.3
3.3   3.5

Answer 1

We input the data set in MS Excel and use the STDEV and COUNT functions to calculate the sample standard deviation and the sample size respectively.



(c) From the two confidence intervals, we observe that their ranges overlap with each other and also the width of their confidence intervals is almost the same. This tells us that the standard deviations of student evaluation ratings of courses and​ professors are not significantly different.