Question

5. An epidemiological study looked at the relationship between earbud use and hearing loss. Data for number of earbud users appear in the table below. Test for an association betweern earbud use and hearing loss at the 5% level of significance. (4 points) Daily Earbud Use (min.) Hearing Loss> 60 60-120 120-180 >180 None Slight Moderate 562 89 698 90 26 239 29 201

Answer 1

here null hypothesis:Ho: earbud use time and hearing loss are not related

alternate hypothesis:Ha:  earbud use time and hearing loss are related

degree of freedom =(row-1)*(column-1)=(3-1)*(4-1)=6

for 6 df and 0.05 level of significance ; critical value $\chi ^{2}$ =12.592

applying chi square test of independence:

Observed	OBS	<60	60-120	120-180	>180	Total
	none	27	19	6	6	58
	slight	35	27	10	10	82
	moderate	26	18	10	10	64
	Total	88	64	26	26	204
Expected	Ei=?row*?column/?total	<60	60-120	120-180	>180	Total
	none	25.020	18.196	7.392	7.392	58
	slight	35.373	25.725	10.451	10.451	82
	moderate	27.608	20.078	8.157	8.157	64
	Total	88	64	26	26	204
chi square	=(Oi-Ei)2/Ei	<60	60-120	120-180	>180	Total
	none	0.16	0.04	0.26	0.26	0.72
	slight	0.00	0.063	0.019	0.019	0.11
	moderate	0.09	0.215	0.416	0.416	1.14
	Total	0.25	0.31	0.70	0.70	1.964

for test statistic 1.964 is less than crtiical value; we fail to reject null hypothesis

we do not have evidence to conclude that earbud use and hearing loss are related,