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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5 - Problem 6se
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5 - Problem 6se

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# Refer to Exercise 5. Additional pieces of yarn will be

ISBN: 9780073401331 38

## Solution for problem 6SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Problem 6SE

Problem 6SE

Refer to Exercise 5. Additional pieces of yarn will be sampled in order to improve the precision of the confidence interval. Which would increase the precision the most: sampling 50 additional pieces of yarn from the old batch, 50 additional pieces from the new batch, or 25 additional pieces from each batch?

Step-by-Step Solution:

Step 1 of 1:

In this question, we are asked to improve the precision of the confidence interval while referring to exercise 5.

Which would increase the precision the most:

sampling 50 additional pieces of yarn from the old batch, 50 additional pieces from the new batch, or 25 additional pieces from each batch.

and

Here  and are variable.

Then 90% confidence interval for the difference  is,

Width of confidence interval =

Case 1: sampling 50 additional pieces of yarn from the old batch.

Hence the sample sizes are  and

The width of a confidence interval is , and the confidence interval is .

Case 2: sampling 25 additional pieces from each batch.

Hence the sample sizes are  and

The width of a confidence interval is , and the confidence interval is .

Case 3: sampling 50 additional pieces of yarn from the new batch.

Hence the sample sizes are  and

The width of a confidence interval is , and the confidence interval is .

So from the above cases, case (3) has the width of while other two case (1) and (2) and has the width of 0.416 and 0.378 respectively.

We know that the width of a confidence interval indicates the precision. Narrow confidence intervals show precise knowledge of parameters, while wide confidence interval shows imprecise knowledge.

Hence 50 additional pieces sampled from the new batch (case 3)  will increase the precision of the confidence interval.

Step 2 of 1

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