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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5 - Problem 13se
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5 - Problem 13se

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

ISBN: 9780073401331 38

Solution for problem 13SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Problem 13SE

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:

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),

, and width

width

Since we want 99% confidence interval, then a level is

and

Then for  is , hence

Now we will find out the number of samples for given mean to be within .

width

Hence the number of sample for given mean to be within  is 92.

Step 2 of 1

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