SOLUTION: A new car is designed to run a mean of at least 50 000 kilometres before its first tune-up. Tests with 30 cars show a sample mean of 49 500 kilometres and a sample standard deviati

Question 264516: A new car is designed to run a mean of at least 50 000 kilometres before its first tune-up. Tests with 30 cars show a sample mean of 49 500 kilometres and a sample standard deviation of 1000 kilometres.
a.
Develop the null and alternative hypotheses most appropriate for testing the claim that the new car can run at least 50 000 kilometres before its first tune-up.
b.
Using a .05 level of significance, test whether or not there is sufficient evidence to reject the claim of a mean of at least 50 000 kilometres.
c.
What is the p-value.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A new car is designed to run a mean of at least 50 000 kilometres before its first tune-up. Tests with 30 cars show a sample mean of 49 500 kilometres and a sample standard deviation of 1000 kilometres.
a.
Develop the null and alternative hypotheses most appropriate for testing the claim that the new car can run at least 50 000 kilometres before its first tune-up.
Ho: u >= 50.000
Ha: u < 50,000
b.
Using a .05 level of significance, test whether or not there is sufficient evidence to reject the claim of a mean of at least 50 000 kilometres.
test statistic: t(49,5000) = (49500-50,000)/[1000/Sqrt(30)] = -2.7386...
critical value: invT(0.05,df=29) = -1.6991..
Conclusion: Since the ts is to the left of the cv, reject Ho.
---------------------------
c.
What is the p-value.
p-value = P(t<-1.6991 when df = 29) = tcdf(-100,-2.7386,df=29) = 0.00522
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Cheers,
Stan H.

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