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 Họ: µ = 2.5 versus H: µ #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 Họ: µ = 2.5 versus Hj: µ # 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?
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 Họ: µ = 2.5 versus Hj: µ # 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?
Question 1
a. nz 15
Question 2
b.n =24
v Question 3
C. Fail to reject Ho. There is no sufficient evidence to
support the claim that the mean wear of crankshafts
Question 4
differs from 2.5 at a = 0.05
d.0.2670
e. Reject Ho. There is evidence to support the claim that
the mean wear differs from 2.5 at a = 0.05
f. Mean wear of crankshafts
g. 0.7330
Transcribed Image Text:Question 1 a. nz 15 Question 2 b.n =24 v Question 3 C. Fail to reject Ho. There is no sufficient evidence to support the claim that the mean wear of crankshafts Question 4 differs from 2.5 at a = 0.05 d.0.2670 e. Reject Ho. There is evidence to support the claim that the mean wear differs from 2.5 at a = 0.05 f. Mean wear of crankshafts g. 0.7330
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