11.2. Hypothesis Test: Multinomial
Population
General Case:
Suppose
there are K populations. We want to test
vs.
where
We
also have the following information:
total sample size: 
observed numbers: 
.
In
addition, as 
is true, the
expected numbers are
expected numbers: 
Chi-Square Test:
The
chi-square test with level of significance 
for
vs
is to
,
where
,
can be obtained by 
,
and where 
is the random variable
distributed as chi-square distribution with degrees of 
In
addition, 
.
Example 2:
The
following data are the frequencies of products of throwing a dice 120 times:
|
Point |
1 |
2 |
3 |
4 |
5 |
6 |
|
Frequency |
13 |
24 |
18 |
22 |
19 |
24 |
Please
test if the dice is fair (i.e., 
) with 
.
[solution:]
Then,
Since
,
we do not
reject .
JavaStatSoft:
Chi-square
test:
Statistics
-> Tests -> Chi-Square Tests -> Hypothesis Test: Multinomial
Population