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	28	11	14
B	26	24	40

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 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.
• There is 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

	X	Y	Z	Total
A	28	11	14	53
B	26	24	40	90
Total	54	35	54	143

(a) Enter the expected frequencies below:

Expected value = r total* c total / overall Total

Eg: X and A = 53 * 54 / 143

expected	X	Y	Z	Total
A	20.014	12.972	20.014	53
B	33.986	22.028	33.986	90
Total	54	35	54	143

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

	X	Y	Z
A	3.1866	0.29979	1.8071
B	1.8765	0.17654	1.0642

      Test Statistic: χ2=

test Stat = 8.4108

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

. df = (r -1) * (c -1) ...................... r = no. of rows and c = no. of columns

= 1 * 2

= 2

Critical Value: C.V. =

=

CV. = 9.2103   .................using chi-square tables

Null: The row and col are independent

Alternative: The row and col are not independent that is they are dependent.

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

Since |Test stat| < C.V.

we do not reject the null hypothesis at 1%.

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