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	51	19	43
B	42	19	39

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=

(c) What is the critical value for this test of independence when using a significance level of αα = 0.025?
      Critical Value: χ2=

(d) What is the correct conclusion of this hypothesis test at the 0.025 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 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.

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

Answer 1

Test Statistic

O : Observed Frequency

E: Expected Frequency

Observed Counts/Frequency	X	Y	Z	Row Total
A	51	19	43	113
B	42	19	39	100
Column Total	93	38	82	213

(a) Enter the expected frequencies

E: Expected Count/Frequency	X	Y	Z
A	(113*93) / 213	(113*38) / 213	(113*82) / 213
B	(100*93) / 213	(100*38) / 213	(100*82) / 213

E: Expected Count/Frequency	X	Y	Z
A	49.338	20.160	43.502
B	43.662	17.840	38.498

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

O	E	O-E
51	49.3380	1.6620	2.7622	0.0560
19	20.1596	-1.1596	1.3447	0.0667
43	43.5023	-0.5023	0.2524	0.0058
42	43.6620	-1.6620	2.7622	0.0633
19	17.8404	1.1596	1.3447	0.0754
39	38.4977	0.5023	0.2524	0.0066
			Total	=0.2737

      Test Statistic: = 0.274

(c) What is the critical value for this test of independence when using a significance level of = 0.025?

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

For 2 degrees of freedom, Critical value : for : 0.025 = 7.378

Critical Value: =7.378

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

As value of the test statistic : = 0.274 < Critical Value: =7.378 ; Fail to reject the null hypothesis.

There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent.

Correction :

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

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(0 - E)

(O - E2/E

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