Question

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

	X	Y	Z
A	30	17	36
B	38	21	30

Give all answers rounded to 3 places after the decimal point, if necessary.

(a) Enter the expected frequencies below:

	X	Y	Z
A
B

(b) What is the chi-square test-statistic for this data?
      Test Statistic: χ2=χ2=

(c) What is the critical value for this test of independence when using a significance level of αα = 0.05?
      Critical Value: χ2=χ2=  

(d) What is the correct conclusion of this hypothesis test at the 0.05 significance level?

• There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.
• There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.
• There is sufficient evidence to support the claim that the row and column variables are dependent.
• There is not sufficient evidence to support the claim that the row and column variables are dependent.

Answer 1

Solution

To test the hypothesis

Ho :Row variables and columns variables are independent.

Vs

Ha : Row variables and columns variables are dependent.

a) Expected frequency table

	X	Y	Z	Total
A				83
B				89
Total	68	38	66	172

Oi	ei	(oi-ei)	(oi-ei)^2
30	32.814	-2.814	7.919	0.241
38	35.186	2.814	7.919	0.225
17	18.337	-1.337	1.788	0.098
21	19.663	1.337	1.788	0.091
36	31.849	4.151	17.231	0.0541
30	34.151	-4.151	17.231	0.505
Total	272			1.701

Oi =observed frequency and

ei = Expected frequency

Test statistic

Test statistic

C) The degree of freedom m= 2 number of row

n= 3 number of columns

DF = (2-1)*(3-1)= 2

The chi square critical value at

from chi square table

Chi square critical value = 5.99

d) decision :

Fail to rejecte Ho

Conclusion : There is insufficient evidence to support the claim that row and column variable are dependent.