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	46	33	49
B	33	14	38

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

(a) Enter the expected frequencies below:

	X	Y	Z
A
B

To find the expected frequencies:

1. Enter the observed matrix into the calculator, per the Technology Corner.
2. Perform the test, per the Technology Corner.
3. Return to the matrix menu and view the B matrix. This will be the expected frequencies.

(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=  (Enter 4.605 as the answer to this question.)

(d) What is the correct conclusion of this hypothesis test at the 0.10 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 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.

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

Answer 1

a)

Expected	Ei=row total*column total/grand total	x	y	z
	A	47.474	28.244	52.282
	B	31.526	18.756	34.718

b)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	x	y	z	Total
	A	0.046	0.801	0.206	1.0526
	B	0.069	1.2059	0.3102	1.5851
	total	0.1147	2.0067	0.5162	2.638
test statistic X2 =		2.6376~ 2.638

c)

for 2 df and 0.1 level , critical value       χ2=

4.605

d)

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