Math 311, Winter 2010, Lab X
The Tools
In this section you’ll learn the mechanics of χ2-tests
 2 - tests for fun and profit: Recall that in class we examined the following data
set regarding the weight classification of 4208 7th – 12th graders who participated in a national
study of adolescent attitudes and behaviours:
Two-way
Table
Male
Female
Total
92
81
173
Normal
1376
1528
2904
Risk of Overwt
279
324
603
Overweight:
280
248
528
Total:
2027
2181
4208
Underweight
We were, in fact, interested in determining if the weight classifications of males and females
differed. Thus we formed the following hypotheses:
H0: there is no difference in the weight classifications of males and females
HA: there is a difference in the weight classifications of males and females
To decide the question, we performed a  - test by hand. Today we’ll learn how do get Minitab
to do the work for us. So, if you haven’t done so already, open Minitab.
2
1. Enter the data in Minitab so that it looks like this:
C1
Male
92
1376
279
280
C2
Female
81
1528
324
248
a. Notice that there is no need to enter the weight classifications – the first row will
be called (1), the second (2), etc..
b. Also (very important) do not include the totals in
your table.
2. Now select Stat>Tables>Chi-Square Test (Two-Way Table in Worksheet)…
3. A window will appear – double click on C1 Male & C2 Female. The box “Columns
containing the table:” should now contain “Male Female.”
4. Select OK and get the following:
Chi-Square Test: Male, Female
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Male
92
83.33
0.901
Female
81
89.67
0.837
Total
173
2
1376
1398.86
0.374
1528
1505.14
0.347
2904
3
279
290.47
0.453
324
312.53
0.421
603
4
280
254.34
2.589
248
273.66
2.406
528
Total
2027
2181
4208
1
Chi-Sq = 8.328, DF = 3, P-Value = 0.040
Make certain that you can identify each number this table!!! We
talked about each in class. If you can’t, ask me!
Since the P-value is sufficiently small (p < 0.05), we may conclude that there is a difference in
the distribution of the weight classifications for males and females.
note: we may not conclude more than “there is a
difference/relationship.”
Okay, that’s it. Chi-squared tests are pretty easy in Minitab. So now it’s your turn to hone the
mad skills learned above.
The Questions
!!!BE CERTAIN TO READ EACH QUESTION CAREFULLY – THEY CONTAIN USEFUL CLUES!!!
1. A study of the relationship between men’s marital status and the level of their jobs used
data on all 8235 male managers and professionals employed by a large manufacturing
firm. Each man’s job has a grade set by the company that reflects the value of that
particular job to the company. The authors of the study grouped the many job grades into
quarters. Grade 1 jobs contain jobs in the lowest quarter of job grades, and grade 4
contains those in the highest quarter. Here are the data:
Marital Status
Job
Grade
1
2
3
4
Single
58
222
50
7
Married
874
3927
2396
533
Divorced
15
70
34
7
Widowed
8
20
10
4
Do these data show a statistically significant relationship between marital status and job
grade?
2. These data record the results of an experiment with acacia trees and ants. Everything
except two species of acacia trees were cleared from an area in Central America. Then
the trees were cleansed of ants using an insecticide. Meanwhile, sixteen colonies of a
particular species of ants were collected elsewhere from other trees of species A. The
colonies were placed roughly equidistant from the trees and allowed to invade them. The
results are summarized in the resulting 2 x 2 table. Do the invasion rates differ for the
two species of trees?
Acacia
Species
A
B
Not
Invaded
92
1376
Invaded
81
1528
By now, it should be understood that you need to explicitly state your hypotheses, the
results of your analysis, and your conclusions!
3. These data come from a report of a survey which investigated whether snoring was
related to various diseases. Those surveyed were classified according to the amount they
snored, on the basis of reports from their spouses. These particular data relate to the
presence or absence of heart disease. Is there a relationship between that amount of
snoring and heart disease? Explicitly state your hypotheses, the results of your analysis,
and your conclusions!
Heart
Disease
yes
no
non-snorers
24
1355
occasional snorers
35
603
snores nearly every
night
21
192
snores every night
30
224