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	33	24	29
B	72	41	14

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 = 0.01?
      Critical Value: χ2=χ2=  

(d) What is the correct conclusion of this hypothesis test at the 0.01 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 support 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 warrant rejection of the claim that the row and column variables are dependent.

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

Answer 1

Solution:
Given:

Claim :  the row variable and the column variable are dependent in the following contingency table.

	X	Y	Z
A	33	24	29
B	72	41	14

Part a) Find the expected frequencies below:

E_ij = Expected frequencies for i^th row and j^th column

Thus we need to find following table:

	X	Y	Z	Total
A	33	24	29	R1 = 86
B	72	41	14	R2 = 127
Total	C1= 105	C2= 65	C3= 43	N = 213

Thus

	X	Y	Z
A	42.394	26.244	17.362
B	62.606	38.756	25.638

Part b) What is the chi-square test-statistic for this data?

Oij	Eij	Oij^2/Eij
33	42.394	25.687
24	26.244	21.948
29	17.362	48.441
72	62.606	82.804
41	38.756	43.374
14	25.638	7.645
N = 213

Thus

Part c) What is the critical value for this test of independence when using a significance level of α = 0.01?

df = (R-1)X(C-1) = (2-1)X(3-1) =1X2 = 2

df = 2

significance level = 0.01

Critical Value: χ2 = 9.210

Part d) What is the correct conclusion of this hypothesis test at the 0.01 significance level?

Since Chi-square test statistic value = >  Critical Value: χ2 = 9.210, we reject null hypothesis H0:  row variable and the column variable are independent

thus correct conclusion is:
There is sufficient evidence to support the claim that the row and column variables are dependent.