Question

You conducting the claim that variable and the column variable are dependent in the following are a test of the row contingency table A 20 31 24 B 13 72 36 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-statistie for this data? Test Statistic: χ- (c) What is the critical value for this test of independence when using a significance level of a-0.05? Critical Value: x (d) What is the correct conclusion of this hypothesis test at the 0.05 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 not sufficient evidence to warrant rejection of 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. Remember to give all answers rounded to 3 places after the decimal point, if necessary

Answer 1

The expected values are obtained by using MINITAB. Procedure: Click stat > Tables > Chi - square test (Two - way table in worksheet). Enter the X, Y and Z in the columns containg the table. Click on ok. Output: Chi - Square Test X, Y, Z Expected counts are printed below observed counts Chi - Square contributions are printed below expected counts Chi - Sq = 9.958, DF = 2 , P - Value = 0.007 From the MINITAB output, the expected frequencies are \r\n From the MINITAB obtained in part (a), the chi^2 values is 9.958. Critical value. Let m be the number of rows and n be the number of columns chi_alpha, (m - 1) (n - !)^2 = chi_0.05 (2 - 1) (3 - 1)^2 = chi_0.05, 2^2 = 5.990 [From Chi - Square distribution table] State the hypothesis. Null hypothesis: H_0: Row variable and columns variable are independent. Alternative hypothesis: H_a: Row variable and columns variables are not independent. Rejection rule: Reject H_0 if Chi -0 Square > 5.990. Conclusion: