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	430	570	369	54
Nose	901	1308	785	106
Throat	238	318	171	17

(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

applying chi square test:

Observed	Oi	18-29	30-44	45-64	65 and older	Total
	eye	430	570	369	54	1423
	nose	901	1308	785	106	3100
	throat	238	318	171	17	744
	Lawyer	1569	2196	1325	177	5267
Expected	Ei=row total*column total/grand total	18-29	30-44	45-64	65 and older	Total
	eye	423.90	593.30	357.98	47.82	1423
	nose	923.47	1292.50	779.86	104.18	3100
	throat	221.63	310.20	187.17	25.00	744
	Lawyer	1569	2196	1325	177	5267
chi square    χ2	=(Oi-Ei)2/Ei	18-29	30-44	45-64	65 and older	Total
	eye	0.0877	0.9150	0.3393	0.7985	2.141
	nose	0.5466	0.1859	0.0339	0.0319	0.798
	throat	1.2088	0.1961	1.3962	2.5613	5.362
	Lawyer	1.843	1.297	1.769	3.392	8.301

test statistic =8.30

ii)bound for p value 0.20< p value <0.30