Workshop Statistics: Discovery with Data and Fathom
Topic 7: Comparing Distributions II: Categorical Variables
Activity 7-1: Suitability for Politics
(a)
-
political inclination: categorical
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suitability opinion: categorical
(b)
-
explanatory: political inclination
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response: suitability opinion
(c) Answers vary from class to class.
Activity 7-2: Age and Political Interest
(a) 385/1265=.304
(b) 531/1265=.420
(c) 349/1265=.276
(d) 146/385=.379
(e) 192/385=.499
(f) 47/385=.122
(g) fill in the table with (d)-(f)
(h)
(i) The youngest age group has less interest in politics (e.g., higher
proportion of these respondents in the "not much" category than the other
age groups). The older age group has more interest in politics (e.g.,
higher proportion of these respondents in the "very much" category than
the other age groups). The middle age group has a large proportion
of respondents indicating moderate interest in politics.
(j) 146/531=.275
(k) 146/381=.383
(l) 146/1265=.1154
Activity 7-3: Pregnancy, AZT, and HIV
(a) Answers vary from student to student
(b) AZT: 13/164=.079; placebo: 40/160=.25
(c) The proportion of HIV-positive babies among placebo mothers is
about 3.15 times greater than the proportion of HIV-positive babies among
AZT mothers.
(d) The difference between the two groups appears to be significant.
It may be possible that pregnant, HIV-positive women could reduce the chance
of their unborn children contracting the virus by taking AZT during pregnancy.
Activity 7-4: Hypothetical Hospital Recovery Rates
(a) hospital A: .8; hospital B: .9; Hospital B saved the higher
percentage of its patients.
(c) hospital A: .983; hospital B: .967; Hospital A saved
the higher percent of fair condition patients.
(d) hospital A: .525; hospital B: .3; Hospital A saved
the higher percent of poor condition patients.
(e) Hospital B treats more patients in fair condition, while hospital
A treats more patients in poor condition. Since fair patients tend
to survive more often, that number can influence the aggregate proportions
in favor of hospital B, even though hospital A saves more patients in either
category.
(f) Answers may vary from student to student since this is an opinion,
but the logical conclusion is hospital A since a patient is either in fair
or poor condition before treatment, not both.
Activity 7-5: Women Senators
(a)
|
Republicans
|
Democrats
|
row total
|
women
|
3
|
6
|
9
|
men
|
52
|
39
|
91
|
column total
|
55
|
45
|
100
|
(b) Republicans: proportion women=3/55=.055, proportion male=52/55=.945;
Democrats: proportion women=6/45=.133, proportion male=39/45=.867;
The Democrats had a higher proportion of women among their Senators
than the Republicans.
(c)
(d)
The ribbon chart gives more
information than the segmented bar chart because it shows the relative
sizes of the two parties.
(e)
This ribbon chart displays
the relative proportions of the parties within each gender.
(f) A higher proportion of women are democrats rather than republicans,
while a higher proportion of males are republicans. Also, the Democrat
party has a larger proportion of women than the Republican party has.
(g) The variables gender and party are not independent among members
of the 1999 U.S. Senate because there is a difference in the gender breakdown
between the two parties.
(h)
|
Republicans
|
Democrats
|
row total
|
men
|
48
|
32
|
80
|
women
|
12
|
8
|
20
|
column total
|
60
|
40
|
100
|
These number achieve the same gender percentages in both groups: women:
.20 and men .80