Question

A random sample of n1=16 communities in western Kansas gave the following information for people under 25 years of age. x1 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 n2=14 regions in western Kansas gave the following information for people over 50 years old. x2 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 a=0.05 State the null and alternate hypotheses.

Answer 1

x̅1=117.0625, s1=16.76, n1=16

x̅2=100.643, s2=10.21, n2=14

Now,

Null Hypothesis:Ho:μ1=μ2
Alternative Hypothesis:Ha:μ1>μ2

The test statistic is

t=(x̅1-x̅12)/√[s1^2/n1+s2^2/n2]

=(117.0625-100.643)/sqrt(16.76²/16 + 10.21²/14)

=3.28

Given Significance level(α)=0.05

The critical value is |t(0.05,df=n1+n2-2=28)|=1.7 (using:student t table)

Here, Critical Value is less than the Test Static hence reject the null hypothesis

So, there is enough evidence to support the claim and we can conclude that the age group over 50 has a lower rate of hay fever