Question

In: Statistics and Probability

13. A textile fiber manufacturer is investigating a new drapery yarn, which the company claims have...

13. A textile fiber manufacturer is investigating a new drapery yarn, which the company

claims have a mean thread elongation of 24 kilograms with a standard deviation of 0.5

kilograms. The company wishes to test the hypothesis

using a random sample of 4 specimens.

H0: μ =24 against H1: μ<24

(a) What is the type I error probability if the critical region is defined as kilograms?

(b) Find beta for the case where the true mean elongation is 23.24 kilograms.

(c) Find beta for the case where the true mean is 23.5 kilograms.

Solutions

Expert Solution

Answer:

Given that:

A textile fiber manufacture is inversting a new drepery yarn,which the company claims has a mean thread elongation of 24 kilograms with a standard deviation of 0.5.

a)

The required probabillity is

The distribution of the sample mean is approximately normal with the mean and the standard deviation

The z-value that corresponds to the critical value 23.5 is

Therefore,

b) We find as

The distribution of the sample mean is approximately normal with the mean and the standard deviation

The z-value that corresponds to the critical value 23.5 is

Therefore,

  

c)

We find as

The distribution of the sample mean is approximately normal with the mean and the standard deviation

The z-value that corresponds to the critical value 23.5 is

Therefore,

  

orchestra answered 2 years ago
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