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	40	35	14
B	19	30	27

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 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 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.

Answer 1

(a) MINITAB Procedure: Step 1: Choose Stat Tables > Chi-Square Test for Association. Step 2: Select Summarized data in a two-way table. Step 3: In Column containing the table X, Y, Z. Step 3: In Categorical variables, for rows enter Sample. For columns enter Column. Step 4: Click OK. MINITAB output:

Chi-Square Test for Association: Sample, column Rows: Sample Columns: column X Y Z All A 40 35 14 89 31.82 35.06 22.12 B 30 27 76 19 27.18 29.94 18.88 All 59 65 41 165 Cell Contents: Count Expected count Pearson Chi-Square - 11.025, DF - 2, P-Value - 0.004 Expected values А B X 31.824 27.176 Y 35.061 29.939 Z 22.115 18.885 (b) The value of the test statistic is x2 =11.025.

(c) The critical value is 7.378. There is sufficient evidence to support the claim that the row and column variables are dependent