Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Textbook Question
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Chapter 8, Problem 48SE

A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.

  1. a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
  2. b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

a.

Expert Solution
Check Mark
To determine

Find the margin of error for 95% confidence interval.

Answer to Problem 48SE

The margin of error for 95% confidence interval is 4.

Explanation of Solution

Calculation:

The given information is that the mean price charge for a trade of 100 shares at $0 per share by a sample of 54 brokers was $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

b.

Expert Solution
Check Mark
To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Explanation of Solution

Calculation:

From Part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.774,33.77+4)=(29.77,37.77) .

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

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Chapter 8 Solutions

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

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