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	45	33	32
B	17	27	16

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 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 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.

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

Answer 1

Null hypothesis : H_o :  the row variable and the column variable are independent

Alternate hypothesis :H_a :  the row variable and the column variable are dependent

Given,

Observed Counts/Frequency	X	Y	Z	Column Total
A	45	33	32	110
B	17	27	16	60
Row Total	62	60	48	170

(a) Enter the expected frequencies below:

E: Expected Count/Frequency	X	Y	Z
A	(110*62) / 170	(110*60) / 170	(110*48) / 170
B	(60*62) / 170	(60*60) / 170	(60*48) / 170

E: Expected Count/Frequency	X	Y	Z
A	40.118	38.824	31.059
B	21.882	21.176	16.941

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

  

O : Observed Frequency

E : Expected Frequency

O	E	O-E	(O-E)2	(O-E)2/E
45	40.1176	4.8824	23.8374	0.5942
33	38.8235	-5.8235	33.9135	0.8735
32	31.0588	0.9412	0.8858	0.0285
17	21.8824	-4.8824	23.8374	1.0893
27	21.1765	5.8235	33.9135	1.6015
16	16.9412	-0.9412	0.8858	0.0523
			Total	4.2393

Test Statistic: = 4.2393

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

Degrees of freedom = (Number rows -1) x (Number of columns - 1) = (2-1)x(3-1) =1 x 2 =2

For 2 degrees of freedom : = 9.21

Critical Value: = 9.21

(d)

correct conclusion of this hypothesis test at the 0.01 significance level

As

As Test Statistic : 4.2393 is less than Critical Value: = 9.21 ( 4.2393 < 9.21); Fail to Reject the Null Hypothesis.

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