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	38	23	30
B	34	33	31

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 = 0.10?
      Critical Value: χ2=χ2=  

(d) What is the correct conclusion of this hypothesis test at the 0.10 significance level?

a)There is sufficient evidence to support the claim that the row and column variables are dependent.

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

c)There is not sufficient evidence to support the claim that the row and column variables are dependent.

d)There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

Answer 1

	X	Y	Z	Total
A	38	23	30	91
B	34	33	31	98
Total	72	56	61	189

a) E: Expected frequency.
E = ( Row total*Column total) / Grand total

	X	Y	Z
A	34.667	26.963	29.370
B	37.333	29.037	31.630

b) Test statistic is

O: Observed frequency
E: Expected frequency.

O	E	(O-E)	(O-E)^2	(O-E)^2/E
38	34.667	3.333333	11.11111	0.320513
23	26.963	-3.96296	15.70508	0.582468
30	29.370	0.62963	0.396433	0.013498
34	37.333	-3.33333	11.11111	0.297619
33	29.037	3.962963	15.70508	0.540864
31	31.630	-0.62963	0.396433	0.012534
			Total	1.77

c) Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (3 - 1) = 1 * 2 = 2

Level of significance = 0.10

Critical value = 4.602

d) Test statistic < critiical value we fail to reject null hypothesis.

Correct option is

c)There is not sufficient evidence to support the claim that the row and column variables are dependent.