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Statistics / Mathematical Statistics with Applications 7 / Chapter 10 / Problem 38E

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

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Refer to Exercise 10.20. The steel is sufficiently hard to

Chapter 10, Problem 38E

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QUESTION:

Problem 38E

Refer to Exercise 10.20. The steel is sufficiently hard to meet usage requirements if the mean Rockwell hardness measure does not drop below 60. Using the rejection region found in Exercise 10.20, find β for the specific alternative μa = 60.

Reference

The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of penetration. For 50 specimens of an alloy of steel, the Rockwell hardness index averaged 62 with standard deviation 8. The manufacturer claims that this alloy has an average hardness index of at least 64. Is there sufficient evidence to refute the manufacturer’s claim at the 1% significance level?

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QUESTION:

Problem 38E

Refer to Exercise 10.20. The steel is sufficiently hard to meet usage requirements if the mean Rockwell hardness measure does not drop below 60. Using the rejection region found in Exercise 10.20, find β for the specific alternative μa = 60.

Reference

The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of penetration. For 50 specimens of an alloy of steel, the Rockwell hardness index averaged 62 with standard deviation 8. The manufacturer claims that this alloy has an average hardness index of at least 64. Is there sufficient evidence to refute the manufacturer’s claim at the 1% significance level?

ANSWER:

Step 1 of 2

According to the reference of question

The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of penetration. For specimens of an alloy of steel, the Rockwell hardness index averaged with standard deviation 8. The manufacturer claims that this alloy has an average hardness index of at least . Is there sufficient evidence to refute the manufacturer’s claim at the significance level. Then the rejection can be defined as;

Reject if

It is given that the sample size, sample mean with standard deviation as

Thus, the rejection region express as;

Reject if

Reject if

Reject if

Reject if

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