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A 99% confidence interval for a population mean based on a

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

Solution for problem 13SE 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 13SE

A 99% confidence interval for a population mean based on a sample of size 64 is computed to be (16.3, 18.7). How large a sample is needed so that a 99% confidence interval will specify the mean to within ±1.0?

Step-by-Step Solution:

Answer:

Step 1 of 1:

In this question, we are asked to find the number of samples needed so that a  confidence interval will specify the mean to within .

A confidence interval for a  population mean based on a sample of size 64 is computed to be .

Let be a large sample of size  from a population with mean and standard deviation  

then a level  confidence interval for  is

……………..(1)

Given level of confidence , sample size , and confidence interval .

An upper confidence bound =  and lower confidence bound

We know from equation (1),

Mean  width = confidence interval

 width = an upper confidence bound

 width = lower confidence bound

 width = 18.7   …………(2)

          width = 16.3    ……………….(3)

On solving equation (2) and (3),

Step 2 of 3

Chapter 5, Problem 13SE is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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