Question

A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test.

		Noise Level
		Low	Medium	High
Exam	Pass	20	17	9	46
	Fail	9	7	12	28
		29	24	21	N = 74

(a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)
$$ \chi_{obt}^2 $$ =

Decide whether to retain or reject the null hypothesis.

Retain the null hypothesis. Reject the null hypothesis.    

(b) Compute effect size using Cramer's V. (Round your answer to two decimal places.)
V =

Answer 1

Observed Values: 1 c1 R1 20 R2 9 Column Total 29 C2 17 7 24 C3 9 12 21 Row Total 46 28 74 / Expected Values = [(Row total x Column total)/Grand total] C1 C2 C3 R1 18.027 14.9189 13.0541 10.973 9.08108 7.94595

20 E CO-E)?/E 18.027 0.2159 10.973 0.3547 14.91890.2903 9.08108 0.4769 13.0541 1.2590 7.94595 2.0684 Total 4.67 7 9 12 x? = (0-5) = 4.67 Number of rows = r = 2 Number of columns =C = 3 D.F =(r-1)x(C-1) = 2 Significance level= a = 0.05 Critical Value = 5.9915 (Using Excel command CHIINV(a,D.F)) P-value = 0.0970 (Using Excel command CHIDIST( X2 ,D.F)) Conclusion: Fail to reject HO

V = 4.67 L =0.25 V Nxmin (r – 1,c-1) V74x1