Chapter 9 Homework
Set A
9.8 Time status versus gender for the 20-24 age category. Refer to Exercise 9.7. The table below breaks
down the 20-24 age category by gender.
Gender
Status
Full-time
Part-time
Total
Male
2719
535
3254
Female
2991
680
3671
Total
5710
1215
6925
a) Compute the marginal distribution for gender – find the corresponding proportions. Display the results
graphically.
(b) Compute the conditional distribution of status (this statement “of status” implies that gender will used as the
whole –denominator of fraction) for males and for females. Display the results graphically and comment on
how these distributions differ.
0.9
0.8
0.7
0.6
0.5
Full-time
0.4
Part-time
0.3
0.2
0.1
0
Male
Female
(c) If you wanted to test the null hypothesis that there is no difference between these two conditional
distributions, what would the expected cell counts be for the full-time status row of the table?
Status
Full-time
Male
Female
2683.082 3026.918
Total
5710
(d) Computer software gives X2 = 5.17. Use Excel’s =chidist(f, df) calculator for chi-square to find the P-value (
or use http://www.stat.tamu.edu/~west/applets/chisqdemo.html) and state your conclusions at the 5% level.
P(X2 > 5.17) = chidist(5.17, 1)
= 0.0230
The result shows that we do have evidence that there is an association between the two
variables. You might be asking why there would be since the two bargraphs look identical
for male and female. The answer lies in the power of this test. Our sample size is 6,925,
thus even if there is a small insignificant difference, this test can pick up on that small
difference. So the result is significant at 5%, but it does not mean that the result offers a
practical difference, meaning a large difference.
9.10 Waking versus bedtime symptoms. As part of the study on ongoing fright symptoms due to exposure to
horror movies at a young age, the following table was presented to describe the lasting impact the movies have
had during bedtime and waking life:
Waking Symptons
Bedtime Symptons
Yes
No
Total
Yes
36
33
69
No
33
17
50
Total
69
50
119
(a) What percent of the students have lasting waking-life symptoms?
69/119 = 0.5798
57.98% of students in the study had waking-life symptons.
(b) What percent of the students have both waking' life and bedtime symptoms?
36/119 = 0.3025 30.25% of students suffered from both waking and bedtime symptons.
(c’) Create the conditional distribution of bedtime symptoms (this statement “of bedtime” implies that waking
will used as the whole –denominator of fraction). Create a bar graph. Does the data suggest there is an
association between waking symptoms and bedtime symptoms?
Waking
Symptons
Bedtime Symptons
Yes
No
Conditional Distribution (waking symptons the
whole)
0.7
Total
0.5217 0.66 0.579832
3913 0.34 0.420168
0.4782
6087
1
1
1
Yes
No
Total
0.6
0.5
Yes
0.4
No
0.3
0.2
I can see that the percentage in the No column seem
to be further apart than the yes column.
0.1
0
Yes
No
(c) Test whether there is an association between waking-life and bedtime symptoms. State the null and
alternative hypotheses, the X2 statistic, and the P-value.
The null hypothesis says that there is no association between the bedtime and waking
symptoms.
The alternative says there is an association.
P(X2 > 2.275) = chidist(2.275, 1)
= 0.1315
The result shows that we do not have evidence that there is
n asssociation (relationship) between the waking
symptoms and the bedtime symptoms.
a
You might be asking why since the graph
shows a difference in the second set of bar graphs. The answer most likely lies in the
sample size. This test lacks power to detect the difference between the two, meaning there
probably is a difference but not that much of one, and the test lacks the power to detect
that difference.
9.11 New treatment for cocaine addiction. Cocaine addiction is difficult to overcome. Addicts have been
reported to have a significant depletion of stimulating neurotransmitters and thus continue to take cocaine to
avoid feelings of depression and anxiety. A 3-year study with 72 chronic cocaine users compared an
antidepressant drug called desipramine with lithium and a placebo. (Lithium is a standard drug to treat cocaine
addiction. A placebo is a substance containing no medication, used so that the effect of being in the study but
not taking any drug can be seen.) One-third of the subjects, chosen at random, received each treatment.14
Following are the results:
Cocaine Relapse
Treatment
Yes
No
Desipramine
10
14
Lithium
18
6
Placebo
20
4
(a)Compare the effectiveness of the three treatments in preventing relapse using percents and a bar graph. Write
a brief summary.
Conditional
Cocaine Relapse
Treatment
Desipramine
Lithium
Placebo
Yes
No
0.416667 0.583333
0.75
The table shows the conditional distribution of cocaine relapse
based on (the denominator) the type of treatment they received. I
can see that the percentage of people who relapsed is different for
each group. It looks like the placebo group had the biggest
percentage of relapase while the desipramine group had the least
occurance of relapse.
0.25
0.833333 0.166667
(b) Can we comfortably use the chi-square test to test the null hypothesis that there is no difference between
treatments? Explain.
Expected Count
Cocaine Relapse
Treatment
Yes
No
Total
Desipramine
16
8
24
Lithium
16
8
24
Placebo
16
8
24
Total
48
24
72
Page 536, in the summary explains that we need at least an
expected cell count average of 5 or greater and we meet that
criteria; our average is 12.
(c) Perform the significance test and summarize the results.
The null hypothesis states there is no relationship
between the treatment groups and relapse.
Conditional Distribution Based on Treatment Group
0.9
0.8
The alternative says there is an association.
P(X2 > 10.49998) = chidist(10.49998, 2)
= 0.00542
0.7
0.6
0.5
Yes
0.4
No
0.3
0.2
0.1
0
Desipramine
Lithium
Treatment group
Clearly the result indicates there is a relationship,
since our p-value is 0.00542.
Notice that our sample size is 72, yet the result is
statistically significant unlike the result from the
previous problem, which had 119.
The reason is that the differences are larger and it
also occurred more than once since the treatment had
a factor level of 3.
Placebo