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A new catalyst is being investigated for use in the

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 8SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 8SE

A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99% confidence interval for the mean yield when the new catalyst is used.

Step-by-Step Solution:

Answer:

Step 1 of 1:

In this question, we are asked to find a 99% confidence interval for the mean yield when the new catalyst is used.

The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%.

The yields are independent and approximately normally distributed.

When the sample size is small, and the population is approximately normal, we can use the Student’s t distribution to compute confidence intervals.

Let  be a small random sample from a normal population with mean . then a level  confidence interval for is

……….(1)

Where  is a Student’s  distribution with degrees of freedom, is sample mean, is a sample standard deviation and  is a number of samples.

Hence  ,  and .

For a 99% confidence interval, the value of is,

 

 and

Putting the value into equation (1)

 The value of = 3.250 from t table, hence our equation become,

 

0.725      

Hence a 99% confidence interval for the mean yield when the new catalyst is used is (0.7846, 0.6654). 


   

Step 2 of 1

Chapter 5, Problem 8SE is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 8SE from chapter: 5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 8SE from 5 chapter was answered, more than 580 students have viewed the full step-by-step answer. The answer to “A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99% confidence interval for the mean yield when the new catalyst is used.” is broken down into a number of easy to follow steps, and 61 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: batches, Yield, new, mean, catalyst. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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