You are conducting a test of the claim that the row variable and the column vari

Question

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table. A 2738 16 B 2552 31 Give all answers rounded to 3 places after the decimal point, if necessary (a) Enter the expected frequencies below: X Y Z (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 -0.025? Critical Value: x2- (d) What is the correct conclusion of this hypothesis test at the 0.025 significance level? 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. 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, ifnecessary

Explanation / Answer

Here the given observed table first

(a) Now the expected values will be calculated by

Expected for A and X = Total number of A * Total nnumber of X / Total sample size = 52 * 81 /189 = 22.2857

Expected value table

(b) Chi - square table

X2= (O - E)2 /E

X2 = 3.251

(c) For dF = (3-1) * (2-1) = 2 and alpha = 0.025

X2critical = 7.3778

(d) Here as X2<  X2critical so there is not sufficient evidence to support the claim that the row and column variables are dependent.

X Y Z Total A 27 38 16 81 B 25 52 31 108 total 52 90 47 189

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