Question

The following table is from the publication of Vital and Health Statistics from the Centers for Disease Control and Prevention/National Center for Health Statistics. The individuals in the following table have an eye irritation, a nose irritation, or a throat irritation. They have only one of the three. Is there sufficient evidence to reject the hypothesis that the type of ear, nose, or throat irritation is independent of the age group at a level of significance equal to .05?

	Age (years)
Type of Irritation	18-29	30-44	45-64	65 and Older
Eye	457	587	359	58
Nose	926	1298	783	90
Throat	261	321	179	23

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
_____< p <_____

Answer 1

a) applying chi square test:

Expected	Ei=row total*column total/grand total	18-29	30-44	45-64	65 and older	Total
	eye	449.62	603.33	361.28	46.77	1461
	nose	953.10	1278.92	765.84	99.14	3097
	throat	241.28	323.76	193.87	25.10	784
	total	1644	2206	1321	171	5342
chi square    χ2	=(Oi-Ei)2/Ei	18-29	30-44	45-64	65 and older	Total
	eye	0.1210	0.4418	0.0144	2.6979	3.275
	nose	0.7706	0.2847	0.3843	0.8420	2.282
	throat	1.6124	0.0235	1.1408	0.1751	2.952
	total	2.504	0.750	1.540	3.715	8.509

test statistic =8.51

ii)

0.20 < p value <0.30