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At many large universities there is an
independent student organization that rates the faculty
and publishes these ratings in a book that all students
can purchase. Last year there were 4 professors teaching
Intro Stats at State U: Drs. Arnold, Murphy, Ryan and
Shafer. Each was rated on the GOOD FAIR POOR scale. The
organization that does the ratings knows full well that
many students have trouble in such a course because of a
dislike for anything remotely resembling mathematics.
Just for kicks (and hopefully to make some interesting
conclusions) the rating form also asks each student to
answer the question: Are you a good math student?
Possible anwers are YES and NO. Here are the results.
All Students
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QUALITY OF INSTRUCTION
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| Professor |
GOOD |
FAIR |
POOR |
Totals |
| Ryan |
41 |
21 |
20 |
82 |
| Arnold |
48 |
18 |
15 |
81 |
| Murphy |
43 |
17 |
21 |
81 |
| Shafer |
43 |
17 |
18 |
78 |
| Totals |
175 |
73 |
74 |
322 |
Students Good
at Math
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| |
QUALITY OF INSTRUCTION
|
|
| Professor |
GOOD |
FAIR |
POOR |
Totals |
| Ryan |
25 |
19 |
18 |
62 |
| Arnold |
6 |
8 |
7 |
21 |
| Murphy |
23 |
8 |
10 |
41 |
| Shafer |
7 |
15 |
15 |
37 |
| Totals |
61 |
50 |
50 |
161 |
Students Not
Good at Math
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| |
QUALITY OF INSTRUCTION
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|
| Professor |
GOOD |
FAIR |
POOR |
Totals |
| Ryan |
16 |
2 |
2 |
20 |
| Arnold |
42 |
10 |
8 |
60 |
| Murphy |
20 |
9 |
11 |
20 |
| Shafer |
36 |
2 |
3 |
41 |
| Totals |
114 |
23 |
24 |
161 |
General questions
- How many cases are there?
- How many variables are measured per case? What
are they? Which are quantitative variables? Which
are categorical?
- Which of the variables are response variables?
Which of them are explanatory variables? (Think
of a student who buys the publication. What is
the intended predictive use?)
- What percentage of students are good at math?
Before proceeding, convince yourself that "All
Students" Table is formed by summing the counts in
the other two tables.
Now, analyze each table separately. If you are working
with others, divide labors.
Specific questions for the analysis of the each of
the individual tables.
- Find the marginal distribution for the variable
"quality of instruction." Draw a bar
graph. What information does this tell you?
- For each professor, find the conditional
distribution for the variable
"quality." Construct a segmented bar
chart to simultaneously display these conditional
distributions.
- Make some conclusions!
a) What similarities are there?
b) Rank the four professors. If there are
roughly similar conditional distributions you may
"tie" them.
c) In a choice between Murphy and Schaefer,
who is preferred?
d) In a choice between Ryan and Arnold, who
is preferred?
Compare results.
- Examine your answers to 3c for the Good and Not
Good math students. Is there a conclusion to be
made here? What is the answer to 3c for all
students? Explain how the combined results arise
from the tables that are separated by math
ability.
- Examine you answers to 3d for the Good and Not
Good math students. Is there a conclusion to be
made here? What is the answer to 3d for all
students? Can you explain this?
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