Question 1
You intend to conduct a goodness-of-fit test for a multinomial distribution with 7 categories. You collect data from 74 subjects.
What are the degrees of freedom for the χ2 distribution for this test?
Solution:
We are given
Number of categories = N = 7
Degrees of freedom = df = N - 1 = 7 - 1 = 6
d.f. = 6
Question 2
Solution:
Here, we have to use chi square test for goodness of fit.
Null hypothesis: H0: Data follows the given distribution.
Alternative hypothesis: Ha: Data do not follow the given distribution.
We are given
Number of categories = N = 4
Degrees of freedom = df = N - 1 = 3
Test statistic formula is given as below:
Chi square = ∑[(O – E)^2/E]
Where, O is observed frequencies and E is expected frequencies.
Calculation tables for test statistic are given as below:
Category |
Prob. |
O |
E |
(O - E)^2/E |
A |
0.2 |
35 |
145*0.2 = 29 |
1.24137931 |
B |
0.3 |
30 |
43.5 |
4.189655172 |
C |
0.3 |
34 |
43.5 |
2.074712644 |
D |
0.2 |
46 |
29 |
9.965517241 |
Total |
1 |
145 |
145 |
17.47126437 |
Category |
Observed Frequency |
Expected Frequency |
A |
35 |
29 |
B |
30 |
43.5 |
C |
34 |
43.5 |
D |
46 |
29 |
Total |
145 |
145 |
Test Statistic = Chi square = ∑[(O – E)^2/E] = 17.47126437
χ2 = 17.471
P-value = 0.001
(By using Chi square table or excel)
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