Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
7th Edition
ISBN: 9781337298353
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams
Publisher: South-Western College Pub
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Chapter 11, Problem 23SE

a.

To determine

To find: The point estimate of the variance of the population.

a.

Expert Solution
Check Mark

Answer to Problem 23SE

The point estimate is 900.

Explanation of Solution

Given:

Sample size (n)=20

Sample mean (x¯)=290

Sample standard deviation (s)=30

Formula used:

The formula to compute the confidence interval for population standard deviation is:

  (n1)s2χ2right<σ<(n1)s2χ2left

The formula to compute the confidence interval for the population variance is:

  (n1)s2χ2right<σ2<(n1)s2χ2left

Calculation:

The point estimate of the variance of the population.

  Estimate of population variance =(s)2=(30)2=900

Thus, the required estimate is 900.

b.

To determine

To find: The 90% confidence interval for the population variance.

b.

Expert Solution
Check Mark

Answer to Problem 23SE

The confidence interval is (567, 1690)

Explanation of Solution

Calculation:

Degrees of freedom (df) = (n1)=(201)=19

The critical values can be calculated as follows:

  χ2right=χ2α2,df=χ20.052,19=χ20.025,19=30.144 (Using χ2-table)

  χ2left=χ21α2,df=χ210.052,19=χ20.975,19=10.117 (Using χ2-table)

Substitute the values in the confidence interval formula.

  (n1)s2χ2right<σ2<(n1)s2χ2left(201)90030.144<σ2<(20)90010.117567<σ2<1690

Thus, the obtained confidence interval is (567, 1690)

c.

To determine

To find: The 90% confidence interval for the population standard deviation

c.

Expert Solution
Check Mark

Answer to Problem 23SE

The confidence interval is (23.8, 41.1)

Explanation of Solution

Calculation:

From the above part, it is known that the confidence interval is (567, 1690)

The confidence interval for the population standard deviationis calculated as:

  567<σ2<1690567<σ2<169023.8<σ<41.1

Thus, the required confidence interval is (23.8, 41.1)

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Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)

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