SOLUTION: The Highway Safety Institute conducted test crashes at 6 mph, calculating the costs for the damage caused. The costs for the five test crashes were $7480, $4910, $9050, $6375, and

Question 959326: The Highway Safety Institute conducted test crashes at 6 mph, calculating the costs for the damage caused. The costs for the five test crashes were $7480, $4910, $9050, $6375, and $4275. Use these data to test the claim that the mean cost of a 6mph crash is different from $5000. Use a 5% level of significance.
Determine the critical value(s) Could you please explain it to me - like I was a six year old (can't think of the name of the movie - but that is just how I feel - lol). Thanks so much.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The Highway Safety Institute conducted test crashes at 6 mph, calculating the costs for the damage caused.
The costs for the five test crashes were $7480, $4910, $9050, $6375, and $4275. Use these data to test the claim that the mean cost of a 6mph crash is different from $5000. Use a 5% level of significance to determine the critical value(s).
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Answer was posted yesterday.
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Ho:: u = 5000
Ha:: u # 5000 (claim)
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sample mean = 6418 ; sample std = 1931.56
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Since your sample is < 30 items, use t-values.
Critical t-values for alpha = 5% with 4 degrees of freedom
= invT(0.025,4) = +/-2.7765
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That this means you should reject Ho if the test statistic
is greater than 2.7765 standard deviations above or below
the mean of 5000.
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test stat depends on the mean of the sample
t(6418) = (6418-5000)/[1931.56/sqrt(5)] = 1.6416
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Conclusion:: Since the test stat is only 1.6 standard
deviation above the mean you should fail to reject Ho.
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Conclusion:: The test results do not support the claim that the
mean is different than 5000 at a 5% level of significance.
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Cheers,
Stan H.
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