|
 Practice
Problems
1. Jury Selection (adapted from the Freedman, Pisani,
Purves classic text)
One study of grand juries in Alameda County, California, compared the
demographic characteristics of jurors with the general population, to
see if jury panels were representative. The results for age are shown
below. The investigators wanted to know if the 66 jurors were selected
at random from the population of Alameda County. (Only persons over 21
and over are considered; the county age distribution is known from
Public Health Department data.) The study was published in the UCLA Law
Review.
| Age |
Count-wide % |
# of jurors observed |
# of jurors expected |
(O-E) |
(O-E)2/E |
| 21-40 |
42% |
5 |
|
|
|
| 41-50 |
23% |
9 |
|
|
|
| 51-60 |
16% |
19 |
|
|
|
| over 60 |
19% |
33 |
|
|
|
| Total |
100% |
66 |
|
|
|
Do we have evidence that grand juries are selected at random for the
population of Alameda County?
2. Pre-school Attendance and Pre-algebra
Achievement
(these are contrived data, based on a real study)
In these times of educational reform, attention has been focused on
pre-school for all children. Since many districts are facing budget
cuts, funding pre-school programs may impact other offerings. Before
making their recommendations, administrators in a large urban district
take a random sample of 50 seventh graders and compare the pre-algebra
achievement levels of those who attended pre-school and those who did
not. If achievement is independent of attending pre-school then the
proportions at each level should be equal. Use the counts in the
frequency table to determine if there is an association between
attending pre-school and pre-algebra achievement.
| |
Below grade level |
At grade Level |
Advanced |
| Pre-school |
8 |
6 |
6 |
| No Pre-school |
6 |
15 |
9 |
3. Evaluating Textbooks
Does the new math program improve student performance?
Suppose you take a random sample of 20 students who are using a new
algebra text which features group work and unit summaries and a second
sample of 30 students who are using a more traditional text. You
compare student achievement on the state test given to all students at
the end of the course. Use the frequency table to determine if the
proportions from each group are equal at each performance level.
| |
Below grade level |
At grade level |
Advanced |
| New text |
8 |
6 |
6
|
| Old text |
6 |
15 |
9 |
4. Summary
The practice problems illustrate the three different
Chi-squared tests. Identify each and determine how you can distinguish
among the tests.
5. Remember those depressed people forced to look at sad
pictures in Unit 4? No? Well, a group of subjects were classified by
whether or not they were depressed. All subjects were shown "sad"
pictures and their responses were measured. The researchers were
interested in knowing whether there were a greater proportion of strong
emotional responses among the depressed people than among the
non-depressed people. Should you do a test of homogeneity or a test of
independence? Why?
Check your solutions
here.
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