A manufacturer produces crankshafts for an automobile engine. The crankshafts wear after 100,000 miles (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of n= 15 shafts is tested and i = 2.78. It is known that o = 0.9 and that wear is normally distributed. Question 1: Parameter of interest for this test Question 2: Test Ho:µ = 2.5 versus H;: u + 2.5, a = 0.05 Question 3: What is the power of the test if true u = 3.10

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A manufacturer produces crankshafts for an automobile engine. The crankshafts wear after 100,000 miles
(0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of
n= 15 shafts is tested and = 2.78. It is known that o = 0.9 and that wear is normally distributed.
Question 1: Parameter of interest for this test
Question 2: Test Ho: µ = 2.5 versus H1: u + 2.5, a = 0.05
Question 3: What is the power of the test if true u = 3.10
Question 4: Sample size required to detect a true mean of 3.10 if we wanted the power to be at least 0.9?
a. Reject Hn. There is evidence to support the claim that the mean wear
differs from 2.5 at a = 0.05
Question 1
Question 2
b.ns 15
v Question 3
C.n=24
Question 4
d. 0.7330
e. Mean wear of crankshafts
f. Fail to reject Ho- There is no sufficient evidence to support the claim that
the mean wear of crankshafts differs from 2.5 at a = 0.05
g 0.2670
>
Transcribed Image Text:A manufacturer produces crankshafts for an automobile engine. The crankshafts wear after 100,000 miles (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of n= 15 shafts is tested and = 2.78. It is known that o = 0.9 and that wear is normally distributed. Question 1: Parameter of interest for this test Question 2: Test Ho: µ = 2.5 versus H1: u + 2.5, a = 0.05 Question 3: What is the power of the test if true u = 3.10 Question 4: Sample size required to detect a true mean of 3.10 if we wanted the power to be at least 0.9? a. Reject Hn. There is evidence to support the claim that the mean wear differs from 2.5 at a = 0.05 Question 1 Question 2 b.ns 15 v Question 3 C.n=24 Question 4 d. 0.7330 e. Mean wear of crankshafts f. Fail to reject Ho- There is no sufficient evidence to support the claim that the mean wear of crankshafts differs from 2.5 at a = 0.05 g 0.2670 >
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