Question

In a study, 1319 schoolchildren at the age of 12 were random selected to be questioned on the prevalence of symptoms of severe cold. Another 1319 schoolchildren at age 14 were random selected to be questioned on the prevalence of symptoms of severe cold. For schoolchildren of age 12, 356 children were reported to have severe colds in the past 12 months, for schoolchildren of age 14, 468 were reported to have severe colds in the past 12 months. Is there an association between the prevalence of severe cold and the age of 12 and 14?

Please conduct a hypothesis testing using the Chi-square test to justify your conclusion.

Answer 1

Solution
		CALCULATION TABLE
	COLD	NOT COLD	TOTAL
AGE 12	356	963	1319
AGE 14	468	851	1319
TOTAL	824	1814	2638
EXPECTED FREQENCY	E1=	1369*824/2638
			412
O=	OBSERVED FREQUENCY
E=	EXPECTED FREQENCY
DF=	(R-1)(C-1)
DF=	(2-1)(2-1)
DF=	1
LEVEL	5%
H0:	There is  no association between the prevalence of severe cold children of the age of 12 and 14
H1:	There is  an association between the prevalence of severe cold children of the age of 12 and 14
	CALCULATION TABLE				TOTAL
O	356	963	468	851	2638
E	412	907	412	907	2638
O-E	-56	56	56	-56	0
(O-E)2/E	7.6116505	3.4575524	7.61165049	3.45755237	22.1384057
(TEST STATISTICS)
	CHI SQUARE=22.1384
	CRITICAL VALUE OF CHI SQUARE =	3.84
CONCLUSION :
CHI SQUARE=22.1384	(TEST STATISTICS)  is greater than the critical value (3.84)
So we reject null hypothesis H0
and conclude that
There is  an association between the prevalence of severe cold children of the age of 12 and 14