Question

11.2

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 x2 distribution for this test? d.f. = Submit License Question 1. Points possible: 1 Unlimited attempts. You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Ho:PA = 0.2; PB = 0.3; pc = 0.3; PD = 0.2 Complete the table. Report all answers accurate to three decimal places. Observed Expected Category Frequency Frequency A 35 B 30 * с 34 D 46 What is the chi-square test-statistic for this data? What is the P-Value? P-Value

Answer 1

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)