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	20	51
B	10	19	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

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 = 0.05?
      Critical Value: χ2=χ2=  (Enter 5.991 as the answer to this question.)

(d) What is the correct conclusion of this hypothesis test at the 0.05 significance level?

• 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.
• 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)

			X	Y	Z
	A	Observed	28	20	51
		Expected	22.393	22.982	53.625
	B	Observed	10	19	40
		Expected	15.607	16.018	37.375

(b) χ2= 4.674

(c) 5.991

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