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	26	26	47
B	30	26	17

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 = 0.025?
      Critical Value: χ2=χ2=  

(d) What is the correct conclusion of this hypothesis test at the 0.025 significance level?

• 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.
• 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.

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table A26126147 B | 30 | 26 | 17 Give all answers rounded to 3 places after the decimal point, if necessary (a) Enter the expected frequencies below: (b) What is the chi-square test-statistic for this data? Test Statistic: (c) What is the critical value for this test of independence when using a significance level of α-0.025? Critical Value"X- (d) What is the correct conclusion of this hypothesis test at the 0.025 significance level? 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. 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

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Answer 1

	Observed (O)
	X	Y	Z	Total
A	26	26	47	99
B	30	26	17	73
Total	56	52	64	172

a) The expected frequency are

	Expected (E )
	X	Y	Z
A	32.23	29.93	36.84
B	23.77	22.07	27.16

b)

	(O-E)^2/E
	X	Y	Z
A	1.21	0.52	2.80
B	1.63	0.70	3.80

	Observed (O)
	X	Y	Z	Total
A	26	26	47	99
B	30	26	17	73
Total	56	52	64	172
	Expected (E )
	X	Y	Z
A	32.233	29.930	36.837
B	23.767	22.070	27.163
	(O-E)^2/E
	X	Y	Z
A	1.205	0.516	2.804
B	1.634	0.700	3.802