The CAOS (Comprehensive Assessment of Outcomes in Statistics) exam is an online multiple-choice test on concepts covered in a typical introductory statistics course. Students take one version before the start of the course and another version after the course ends. Before and After scores for a possible random sample of 10 students are shown in the table. (An actual random sample of scores are given in Exercise C.68 on page 455 of the text.) Student A B C D E F G H I J Before 43 40 48 65 60 48 43 38 43 55 After 60 45 55 80 85 71 52 35 54 55 a). We are interested in determining whether taking the course increases students’ understanding, as measured by this test. Why should we do a paired design rather than two separate groups? b). Find the differences (After – Before) for all 10 students. State the mean, standard deviation, and sample size for the differences here: c). Test to see if scores at the end of the course are higher, on average, than scores at the beginning of the course. Show all details of the test.
Problem 1: CAOS Comparisons
The CAOS (Comprehensive Assessment of Outcomes in Statistics) exam is an online multiple-choice test on concepts covered in a typical introductory statistics course. Students take one version before the start of the course and another version after the course ends. Before and After scores for a possible random sample of 10 students are shown in the table. (An actual random sample of scores are given in Exercise C.68 on page 455 of the text.)
|
Student |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
|
Before |
43 |
40 |
48 |
65 |
60 |
48 |
43 |
38 |
43 |
55 |
|
After |
60 |
45 |
55 |
80 |
85 |
71 |
52 |
35 |
54 |
55 |
a). We are interested in determining whether taking the course increases students’ understanding, as measured by this test. Why should we do a paired design rather than two separate groups?
b). Find the differences (After – Before) for all 10 students. State the mean, standard deviation, and sample size for the differences here:
c). Test to see if scores at the end of the course are higher, on average, than scores at the beginning of the course. Show all details of the test.
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