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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:

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), , 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

##### ISBN: 9780073401331

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