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 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 =

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)

X2obt =5.24

Retain the null hypothesis

\b)

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