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A manufacturer produces crankshafts for an automobile
Chapter 9, Problem 43E(choose chapter or problem)
A manufacturer produces crankshafts for an automobile engine. The crankshafts wear after 100,000 miles 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 \(\bar{x}=2.78\). It is known that \(\sigma=0.9\) and that wear is normally distributed.
(a) Test \(H_0:\ \mu=3\) versus \(H_1:\ \mu\ne3\) using \(\alpha=0.05\).
(b) What is the power of this test if \(\mu=3.25\)?
(c) What sample size would be required to detect a true mean of if we wanted the power to be at least
?
Equation Transcription:
Text Transcription:
n=15
x bar=2.78
sigma=0.9
H_0:mu=3
H_1:mu not=3
alpha=0.05
mu=3.25
Questions & Answers
QUESTION:
A manufacturer produces crankshafts for an automobile engine. The crankshafts wear after 100,000 miles 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 \(\bar{x}=2.78\). It is known that \(\sigma=0.9\) and that wear is normally distributed.
(a) Test \(H_0:\ \mu=3\) versus \(H_1:\ \mu\ne3\) using \(\alpha=0.05\).
(b) What is the power of this test if \(\mu=3.25\)?
(c) What sample size would be required to detect a true mean of if we wanted the power to be at least
?
Equation Transcription:
Text Transcription:
n=15
x bar=2.78
sigma=0.9
H_0:mu=3
H_1:mu not=3
alpha=0.05
mu=3.25
ANSWER:
Step 1 of 6
Given,
Sample size, n = 10
The sample mean,
The standard deviation,
Using the given values let’s determine the following: