Question

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table. х Y Z A 42 39 27 B 37 32 32 Give all answers rounded to 3 places after the decimal point, if necessary. (a) Enter the expected frequencies below: х Y Z A B (b) What is the chi-square test-statistic for this data? Test Statistic: x? (c) What is the critical value for this test of independence when using a significance level of a = 0.005? Critical Value: x (d) What is the correct conclusion of this hypothesis test at the 0.005 significance level? There is 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

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Answer 1

lel, the observed frequency is given by, U х Y Z IRI A 39 42 37 79 27 32 Total 108 10) n=log B 32 Total 59 I find Expected frequency, Eij= Rix g A B Total x 7 Z 40.823 36.689 30,488 138.177 34,311 28,512 99 59 Total 108 101 n=209 b) The test statistic, x² EE Coij- Eij)? Eij 12 (42-40.823) (39-36.689)? + 40.823 36,689 (27-30.488)2( 37-38.177) + 30.488 38,177 ( 32-34,311)² (32-28,51) + + 34,31 28,512 2 2 2 ² = 1,197

a critical value of 22 at p= 0.005 f df = (0-1) (0-1)=(2-1) (3-1) 1 X2 = 2 Critical value x²= 10.597 d) conclusions Cael. x < critical x² Hence fail to reject the null hypothesis at 0.005 significance level, There is not sufficient evidence to support the claim that the now & column vanables are dependent. option. (d) is correct,