A random sample of 17 residents of Delaware County in Pennsylvania has a mean an

Question

A random sample of 17 residents of Delaware County in Pennsylvania has a mean annual income of $35800 and a standard deviation of $7800. In Greene County Pennsylvania, a random sample of 18 residents has a mean annual income of $35100 and standard deviation of $7375. Test the claim at a = 0.01 that the mean annual incomes in Delaware and Greene Counties are not the same. Assume the population variances are equal.

a. Identify the claim and state Ho and Ha
b. find the critical value(s) and identify the rejection region(s)
c. find the standardized test statistic
d. decide whether to reject or fail to reject the null hypothosis
e. interpret the decision in the context of the original claim.
Assume the populations have approximately normal distributions

Explanation / Answer

Delaware: n1=17, xbar1=35800, s1=7800
Greene: n2=18, xbar2=35100, s2=7375

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a. Identify the claim and state Ho and Ha

Ho:1=2

Ha: 1 not equal 2

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b. find the critical value(s) and identify the rejection region(s)

Given a=0.01, the critical value is t(0.005, df=n1+n2-2 =17+18 - 2 =33) =2.73 (check student t table)

If t<-2.73 or t> 2.73 , we reject Ho

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c. find the standardized test statistic

t=(xbar1 -xbar2)/[s1^2/n1 +s2^2/n2]

=(35800-35100)/sqrt(7800^2/17 +7375^2/18 )

= 0.27

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d. decide whether to reject or fail to reject the null hypothosis

Since t= -2.73<0.27<2.73, we do not reject Ho.

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e. interpret the decision in the context of the original claim.

So we can not conclude that the mean annual incomes in Delaware and Greene Counties are not the same.

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