Rates in Morbidity Among Blacks

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                                        91%                             17%
Whites                                         9%                             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)    Gender and happiness are independent.
 Gender and happiness are dependent.
3)  
4)   P-value: 0.87
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)  1.70 + 8.18 + 1.27 + 6.11 = 17.3.

11.29 Prison and gender:
a) 832/100,000 = 0.00832 of men were incarcerated, whereas 58/100,000 = 0.00058. 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.
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.