Solutions - Categorical Variables
11.3 FBI statistics:
a) These distributions refer to those of x at given categories of y.
RACE OF VICTIM
RACE OF MURDERER
Blacks
Whites
Blacks
Whites
91%
9%
17%
83%
b) x and y are dependent because the probability of a murderer being of a certain race changes
greatly according to the race of the person murdered.
11.9 Happiness and gender:
1) The assumptions are that there are two categorical variables (gender and happiness in this
case), that randomization was used to obtain the data, and that the expected count was at least
five in all cells.
2) H 0 : Gender and happiness are independent.
H a : Gender and happiness are dependent.
 Observed Count  Expected Count 
2
3)  2 
Expected Count
 0.80
4) P-value: 0.67
5) The P-value is quite large. If the null hypothesis were true, the probability would be 0.67
of getting a test statistic at least as extreme as the value observed. It is plausible that the
null hypothesis is true, and that gender and happiness are independent. With a
significance level of 0.05, we could not reject the null hypothesis.
11.11 Life after death and gender:
a) BELIEF IN LIFE AFTER DEATH
GENDER
Yes
No
Total
Males
891
233
1124
Females
1286 219
1505
b) BELIEF IN LIFE AFTER DEATH
GENDER
Yes
No
Total
Males
930.75 193.25 1124
Females
1246.25 258.75 1505
There are more women who believe in the afterlife and men who do not than is expected.
c)
 Observed Count  Expected Count 

2

2
Expected Count
2
2
2



891 - 930.75
233 - 193.25
1286 - 1246.2



930.75
193.25
1.70 + 8.18 + 1.27 + 6.11 = 17.3.
11.29 Prison and gender:
a) 917/100,000 = 0.00917 of men were incarcerated, whereas 64/100,000 = 0.00064. The
relative risk of being incarcerated is 0.00832/0.00058 = 14.3. Men were 14.3 times as
likely as women were to be incarcerated.
1246.2


b) The difference of proportions being incarcerated is 0.00832 – 0.00058 = 0.008. The
proportion of men who are incarcerated is 0.008 higher than the proportion of women
who are incarcerated.
c) The response in part (a) is more appropriate because it shows there is a substantial
gender effect, which the difference does not show when both proportions are close to 0.
10.43 Female for President?:
a)
VOTE
SEX
Yes
No
Total
Females
94%
6%
100%
Males
94%
6%
100%
b) If results for the entire population are similar, it does seem possible that gender and opinion
about having a woman President are independent. The percentages of men and women who
would vote for a qualified woman may be the same.