Question

A random sample of communities in western Kansas gave the following information for people under 25 years of age. Rate of hay fever per 1000 population for people under 25 124 96 98 107 120 122 142 136 112 124 81 124 108 120 144 115 A random sample of regions in western Kansas gave the following information for people over 50 years old. : Rate of hay fever per 1000 population for people over 50 87 103 100 98 105 98 106 117 83 105 99 86 117 105 Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use State the null and alternate hypotheses.

Answer 1

	Under 25 Years ( X )		Over 50 years ( Y )
	25	7507.7199	50	2234.1409
	124	152.5941	87	105.4051
	96	244.8317	103	32.8707
	98	186.2433	100	7.4709
	107	21.5955	98	0.5377
	120	69.7709	105	59.8039
	122	107.1825	98	0.5377
	142	921.2985	106	76.2705
	136	593.0637	117	389.4031
	112	0.1245	83	203.5387
	124	152.5941	105	59.8039
	81	939.2447	99	3.0043
	124.0	152.5941	86	126.9385
	108	13.3013	117	389.4031
	120	69.7709	105	59.8039
	144	1046.7101
	115	11.2419
Total	1898	12189.8817	1459	3748.93

Mean

Standard deviation

Mean

Standard deviation

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 1.8166

Test Criteria :-
Reject null hypothesis if


DF = 26


Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 1.8166 ) = 0.0404
Reject null hypothesis if P value < level of significance
P - value = 0.0404 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that the age group over 50 has a lower rate of hay fever at 5% level of significance.