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Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 ( The Wall Street Journal , October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is σ = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent. b. Develop a 95% confidence interval estimate of the population mean monthly rent. c. Develop a 99% confidence interval estimate of the population mean monthly rent. d. What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

Solutions

Chapter
Section
Chapter 8.1, Problem 10E
Textbook Problem
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Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 (The Wall Street Journal, October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is σ = $650.

  1. a. Develop a 90% confidence interval estimate of the population mean monthly rent.
  2. b. Develop a 95% confidence interval estimate of the population mean monthly rent.
  3. c. Develop a 99% confidence interval estimate of the population mean monthly rent.
  4. d. What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

Expert Solution

a.

To determine

Find the 90% confidence interval for the population mean monthly rent.

Explanation of Solution

Calculation:

The given information is that the mean monthly rent at assisted-living facilities are increase 17% over the last five years is $3,486 and the population standard deviations is $650.

The formula for confidence interval for population mean is,

x¯±zα2σn

From the “Table 8.1 value of zα2”, the value of zα2 for 90% is 1.645.

The value of confidence interval for population mean is,

x¯±zα2σn=3,486±1

Expert Solution

b.

To determine

Find the 95% confidence interval for population mean monthly rent.

Expert Solution

c.

To determine

Find the 99% confidence interval for population mean monthly rent.

Expert Solution

d.

To determine

Explain the width of the confidence level when the increase of confidence level.

Check whether it is reasonable or not.

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Chapter 8 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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