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Get Full Access to Statistics For Business And Economics - 12 Edition - Chapter 6 - Problem 5e
Get Full Access to Statistics For Business And Economics - 12 Edition - Chapter 6 - Problem 5e

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# A random sample of 70 observations from a normally

ISBN: 9780321826237 51

## Solution for problem 5E Chapter 6

Statistics for Business and Economics | 12th Edition

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Problem 5E

Problem 5E

A random sample of 70 observations from a normally distributed population possesses a sample mean equal to 26.2 and a sample standard deviation equal to 4.1.

a. Find an approximate 95% confidence interval for μ.

b. What do you mean when you say that a confidence coefficient is .95?

c. Find an approximate 99% confidence interval for μ.

d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?

e. Would your confidence intervals of parts a and c be valid if the distribution of the original population was not normal? Explain.

Step-by-Step Solution:

Step 1 of 5

(a)

Given a random sample of  observations which follows a normally distributed population.

Given sample mean  and sample standard deviation

We are asked to find an approximate  confidence interval for

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

then a level  confidence interval for  is

……………..(1)

Given sample mean  ,  sample standard deviation  and

Since we want 95% confidence interval, then a level is

and

Then for  is , hence

Hence 95% confidence interval for is

Hence  a 95% confidence interval for  is .

Step 2 of 5

Step 3 of 5

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