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 20 44 34 B 17 34 21 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: χ 2 = (c) What is the critical value for this test of independence when using a significance level of α = 0.10? Critical Value: χ 2 = (d) What is the correct conclusion of this hypothesis test at the 0.10 significance level? 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 not sufficient evidence to warrant rejection of 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

(a)

Observed Frequencies:

	X	Y	Z	Total
A	20	44	34	98
B	17	34	21	72
Total	37	78	55	170

Expected Frequencies:

Observed Frequencies:

	X	Y	Z	Total
A	37X98/170=2133	44.96	31.71	98
B	15.67	33.04	23.29	72
Total	37	78	55	170

(b)

O	E	(O - E)2/E
20	21.33	0.0829
44	44.96	0.0205
34	31.71	0.1654
17	15.67	0.1129
34	33.04	0.0279
21	23.29	0.2252
Total = $\chi ^{2}$ =		0.636

Test statistic = $\chi ^{2}$ = 0.636

(c)

$\alpha$ = 0.10

ndf = (r - 1) X (c - 1)

= (2 - 1)X (3 - 1) = 2

From Table, critical value of $\chi ^{2}$ = 4.605

(d)

Since the calculated value of $\chi ^{2}$ = 0.636 is less than critical value of $\chi ^{2}$ = 4.605, the difference isnot significant. Fail to reject null hypothesis.

Conclusion:

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