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Statistics / Applied Statistics and Probability for Engineers 6 / Chapter 9.2 / Problem 42E

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

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Chapter 9, Problem 42E

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QUESTION:

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 shafts is tested and . It is known that and that wear is normally distributed.

(a) Test versus using .

(b) What is the power of this test if ?

(c) What sample size would be required to detect a true mean of if we wanted the power to be at least ?

Questions & Answers

QUESTION:

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 shafts is tested and . It is known that and that wear is normally distributed.

(a) Test versus using .

(b) What is the power of this test if ?

(c) What sample size would be required to detect a true mean of if we wanted the power to be at least ?

ANSWER:

Step 1 of 5

Given,

Sample size, n = 15

The sample mean,

The standard deviation,

Using the given values let’s determine the following:

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