Question

# A professor tests whether the loudness of noise during an exam (low, medium, and high) is...

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 =

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

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