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 19 16 9 44

Fail 9 6 10 25

28    22 19 N = 69

(a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal place)

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

a)\

Applying Chi square test:

Expected	Ei=row total*column total/grand total	Low	Medium	High	Total
	Pass	17.8551	14.0290	12.1159	44
	Fail	10.1449	7.9710	6.8841	25
	total	28	22	19	69
chi square    χ2	=(Oi-Ei)2/Ei	Low	Medium	High	Total
	Pass	0.073	0.277	0.801	1.1517
	Fail	0.129	0.487	1.410	2.0270
	total	0.2026	0.7643	2.2117	3.1786
test statistic X2 =		3.1786
p value =		0.2041

from above test statistic X² =3.18

since p value >0.05,    retain   the null hypothesis\

b)

Cramer V=φc=√(X2/(n*(k-1)))=

0.21