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A random sample of 70 observations from a normally

Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich ISBN: 9780321826237 51

Solution for problem 5E Chapter 6

Statistics for Business and Economics | 12th Edition

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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich

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:

Answer

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

Chapter 6, Problem 5E is Solved
Step 3 of 5

Textbook: Statistics for Business and Economics
Edition: 12
Author: James T. McClave, P. George Benson, Terry T Sincich
ISBN: 9780321826237

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A random sample of 70 observations from a normally