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
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)
:
0
H
Gender and happiness are independent.
:
a
H
Gender and happiness are dependent.
3)
(
29
80
.
0
2
2
=

=
∑
Count
Expected
Count
Expected
Count
Observed
χ
4) Pvalue: 0.87
5)
The Pvalue 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.
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 '08
 BARROSO,JOAOR
 Statistics, Probability, Null hypothesis, Statistical hypothesis testing

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