Question

Please show using TI-83

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	15	41
B	72	5	31

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 = 0.05?
      Critical Value: χ2=χ2=  

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

• 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.
• 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.

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

Answer 1

The statistical software output for this problem is :

Contingency table results:
Rows: var2
Columns: None

Cell format
Count (Expected count)

	X	Y	Z	Total
A	28 (43.75)	15 (8.75)	41 (31.5)	84
B	72 (56.25)	5 (11.25)	31 (40.5)	108
Total	100	20	72	192

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	2	23.109982	<0.0001

Test statistics = 23.110

Critical value = 5.991

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