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 21 16 8 45 Fail 8 5 10 23 29 21 18 N = 68 (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 $ = Correct: Your answer is correct. Decide whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. Correct: Your answer is correct. (b) Compute effect size using Cramer's V. (Round your answer to two decimal places.) V =

Answer 1

applying chi square test:

Expected	Ei=row total*column total/grand total	low	medium	high	Total
	pass	19.19	13.90	11.91	45
	fail	9.81	7.10	6.09	23
	total	29	21	18	68
chi square    χ2	=(Oi-Ei)2/Ei	low	medium	high	Total
	pass	0.1705	0.3182	1.2846	1.773
	fail	0.3336	0.6226	2.5134	3.470
	total	0.504	0.941	3.798	5.243

a)

X²_obt =5.24

Retain the null hypothesis

\b)

Cramer's V =sqrt(X²/n) =sqrt(5.24/68) =0.28