Question 258182: Can you please help me with this problem?
The average mpg usage for a 2004 Ford Expedition 2WD for a sample of 10 tanks of gas was 17.0 with a standard deviation of 0.8. For a Ford Explorer 2WD, the average mpg usage for a sample of 10 tanks of gas was 18.5 with a standard deviation of 1.0.
a) What are the null and alternative hypotheses to test if the 2004 Ford Expedition has lower fuel economy than the 2004 Ford Explorer?
b) Using α = 0.01, what is the critical value for the hypothesis test?
c) What is the test statistic for the hypothesis test?
d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.
e) What is the p-value for the hypothesis test?
Your Help is very much appreciated.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The average mpg usage for a 2004 Ford Expedition 2WD for a sample of 10 tanks of gas was 17.0 with a standard deviation of 0.8. For a Ford Explorer 2WD, the average mpg usage for a sample of 10 tanks of gas was 18.5 with a standard deviation of 1.0.
a) What are the null and alternative hypotheses to test if the 2004 Ford Expedition has lower fuel economy than the 2004 Ford Explorer?
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Note: Lower fuel economy means lower miles per gallon.
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Ho: u(exped)-u(explo) = 0
Ha: u(exped)-u(explo) > 0
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b) Using α = 0.01, what is the critical value for the hypothesis test?
Running a 2-Sample Ttest on a Ti calculator shows the df = 17.1725
You also could use df = 10+10-2 = 18
CV = invT(0.995,df=17.1725) = 2.8946
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c) What is the test statistic for the hypothesis test?
t(18.5-17)= (18.5-17)/sqrt((0.8)^2/10 + (1)^2/10) = 3.704
d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.
Reject Ho
The fuel economy of the Explored and the Expedition are not the same.
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e) What is the p-value for the hypothesis test?
The p-value is P(t > 3.704 when df = 18) = 0.00081206
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Cheers,
Stan H.
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