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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:

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

Step 3 of 5

##### ISBN: 9780321826237

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A random sample of 70 observations from a normally