A manufacturer of four-speed clutches for automobiles claims that the clutch wil
ID: 3369346 • Letter: A
Question
A manufacturer of four-speed clutches for automobiles claims that the clutch will not fail until after 50,000 miles. A random sample of 10 clutches has a mean of 58,750 miles with a standard deviation of 3775 miles. Assume that the population distribution is normal. Does the sample data suggest that the true mean mileage to failure is more than 50,000 miles. Test at the 5% level of significance.
a.
What kind of hypothesis test is this?
One Proportion z-Test
One mean t-test
Two Proportions z-Test
Two mean t-test
Paired Data
b.
What is the value of the hypothesized mean?
c.
What is the value of the sample statistic?
d.
What is the value of the standard error?
Round your answer to 3 decimal places.
e.
What is the p-value?
Do not use scientific notation. Round your answer to 5 decimal places.
f.
What would it mean to make a Type I error?
We concluded that the mean mileage to failure is more than 50,000 miles, when in fact it is not.
We did not conclude that the mean mileage to failure is more than 50,000 miles, when in fact it is.
A.One Proportion z-Test
B.One mean t-test
C.Two Proportions z-Test
D.Two mean t-test
E.Paired Data
Explanation / Answer
SolutionA:
given sample size is n=10
n<30 (small sample)
normal distr
its a
One mean t-test
Solutionb:
value of hypoothesize mean=50000
Solutionc:
t=sample mean-pop mean/samplesd/sqrt(n)
=58750-50000/3775/sqrt(10)
t=7.329
Solutiond:
satandrd error
sample sd/sqrt(n)
=3775/sqrt(10)
=1193.760
ANSWER:1193.760
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