SOLUTION: Please,I really need some help with this problem: The manufacturer of Winston Tire Company (WTC) claims its new tires last for an average 45k miles. An independent testing agenc

Question 129780: Please,I really need some help with this problem:
The manufacturer of Winston Tire Company (WTC) claims its new tires last for an average 45k miles. An independent testing agency road-tested 135 tires to substantiate the claim made by WTC. The sample mean was 44k miles with a sample standard deviation of 4k miles. Using 1% significance, determine if there is a reason to reject the claim made by WTC and conclude that the tires last for less than 45k miles.

Lets do this in an interactive fashion.

First, answer the following questions:

- what is 'n'
- calculate the confidence intervals (using 44k miles as your mean) (1% significance means 99% confidence)

Thanks...
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The manufacturer of Winston Tire Company (WTC) claims its new tires last for an average 45k miles. An independent testing agency road-tested 135 tires to substantiate the claim made by WTC. The sample mean was 44k miles with a sample standard deviation of 4k miles. Using 1% significance, determine if there is a reason to reject the claim made by WTC and conclude that the tires last for less than 45k miles.
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- what is 'n'
Ans: n is the sample size; in your problem that would be 135
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- calculate the confidence intervals (using 44k miles as your mean) (1% significance means 99% confidence)
Ans: The standard error is E= 2.575(4/sqrt(135)) = 7.48..
C.I. is (44-E,44+E)
C.I. is (36.52,51.48)
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Fail to reject the claim since 45K is in the 1% confidence interval.
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Cheers,
Stan H.
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