Workshop Statistics: Discovery with Data, Second Edition

Topic 7: Comparing Distributions II: Categorical Variables

Activity 7-1: Suitability for Politics

(a) (b) (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

(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
men
52
39
91
women
3
6
9
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) There were more Republicans than Democrats in the 1999 U.S. Senate.  There were more total female Senators in the Democratic pary than in the Republican party.  Consequently, the Democrats had a higher proportion of women among their Senators.
(e) 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.
(f)
 
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