Question

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

		Noise Level
		Low	Medium	High
	Pass	19	16	9	44
	Fail	9	5	10	24
		28	21	19	N = 68

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

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) H₀: loudness of noise(Low,Medium,High) and grades(Pass,Fail) are independent.

H_1:loudness of noise(Low,Medium,High) and grades(Pass,Fail) are dedependent.

~_(r-1)(s-1)

	Low	Medium	High	Total
Pass	19	16	9	44
Fail	9	5	10	24
Total	28	21	19	68

E(19)=28*44/68=18.11 (E_ij=corresponding row total*corresponding column total/grand total)

E(9)=28*24/68=9.88

E(16)=21*44/68=13.58

E(5)=21*24/68=7.41

E(9)=19*44/68=12.29

E(10)=19*24/68=6.70

fi	ei	(fi-ei)2/ei
19	18.11	0.0437
9	9.88	0.0783
16	13.58	0.431
5	7.41	0.783
9	12.29	0.880
10	6.70	1.625

=3.841

=3.841~_2,0.05 (calculated value)

_{2,0.05=5.991 (tabulated)}

since, _cal <_tab we accept null hypothesis.

Hence,H₀: loudness of noise(Low,Medium,High) and grades(Pass,Fail) are independen is accepted.

(b) Cramer's V=

=

=

=

=0.2376

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