Use software to test the null hypothesis of whether there is a relationship betw

Question

Use software to test the null hypothesis of whether there is a relationship between the two classifications, A and B, of the 3 times 3 contingency table shown below. Test using alpha = 0.01. (a) chi^2 = (b) Find the degrees of freedom. (c) Find the critical value. chi^2 = (d) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that there is no relationship between A and B. B. We can reject the null hypothesis that A and B are not related and accept that there seems to be a relationship between A and B.

Explanation / Answer

Null Hypothesis : H0: Ai are independent of Bi where i = 1,2,3

Alternative Hypothesis : Ha : Ai are not independent of Bi where i = 1,2,3

Here observed Table

Here expected table

Chi - square table calculated by (Oi - Ei)/ Ei

where Oi is the observed values and Ei are expected value

so (a) X2= 13.109

(b) degrees of freedom = (3-1) * (3-1) = 4

(c) Critical value of X2 for dF = 4 and alpha = 0.01 is 13.277

(d) SO, X2< X2critical so There is not sufficient evidence to reject the null hypothesis and there is no relationship between A and B.

B1 B2 B3 total A1 54 52 75 181 A2 66 67 41 174 A3 75 68 73 216 Total 195 187 189 571

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