A random sample of n_1 = 16 communities in western Kansas gave the following inf

Question

A random sample of n_1 = 16 communities in western Kansas gave the following information for people under 25 years of age. X_1: Rate of hay fever per 1000 population for people under 25 122 82 95 144 115 96 112 108 109 101 121 96 112 112 106 116 A random sample of n_2 =14 regions in western Kansas gave the following information for people over 50 years old. X_2: Rate of hay fever per 1000 population for people over 50 83 104 90 107 116 106 104 89 112 94 97 111 83 104 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 alpha = 0.05 What is the value of the test statistic? -1.436 2.021 -2.021 1.436 0.518

Explanation / Answer

from above

std error of differnce = (s12/n1+s22/n2 )1/2 =4.547

hence test stat t=(X2-X1)/std error =-2.021

for which p value =0.0267

as p value is less then 0.05 level, data conclude that age group over 50 has lower rate of hay fever

S. no child adult 1 122 83 2 82 104 3 95 90 4 144 107 5 115 116 6 96 106 7 112 104 8 108 89 9 109 112 10 101 94 11 121 97 12 96 111 13 112 83 14 112 104 15 106 16 116 total 1747.000 1400.000 mean 109.188 100.000 std deviation(S) 14.110 10.735

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