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	427	570	330	59
Nose	921	1303	806	108
Throat	259	326	172	25

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


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

Reject the null hypothesis, there is significant evidence that this sample contradicts the claim of independence. Reject the null hypothesis, there is not significant evidence that this sample contradicts the claim of independence.     Fail to reject the null hypothesis, there is significant evidence that this sample contradicts the claim of independence. Fail to reject the null hypothesis, there is not significant evidence that this sample contradicts the claim of independence.

You may need to use the appropriate table in Appendix B to answer this question.

Answer 1

applying chi square test:

Expected	Ei=row total*column total/grand total	18-29	30-44	45-64	65 and older	Total
	Eye	419.77	574.41	341.67	50.15	1386
	Nose	950.39	1300.50	773.56	113.55	3138
	Throat	236.84	324.09	192.77	28.30	782
	total	1607	2199	1308	192	5306
chi square    χ2	=(Oi-Ei)2/Ei	18-29	30-44	45-64	65 and older	Total
	Eye	0.1245	0.0338	0.3984	1.5606	2.117
	Nose	0.9088	0.0048	1.3605	0.2713	2.545
	Throat	2.0734	0.0113	2.2386	0.3842	4.707
	total	3.107	0.050	3.997	2.216	9.370

i)from above test statistic =9.370

ii)

0.10 < p value <0.20

b)

Fail to reject the null hypothesis, there is not significant evidence that this sample contradicts the claim of independence.