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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
ISBN: 9781305881884

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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
ISBN: 9781305881884
Textbook Problem

In a study conducted by The Wall Street Journal, 350 large U.S. companies were asked how they compensated their CEOs. One question asked if the companies included stock options in their CEO compensation packages: 70% said they did. Another question asked if the companies provided their CEOs personal use of corporate aircraft: 63% said they did (The Wall Street Journal/Hay Group CEO Compensation Study. 2010).

  1. a. Develop an estimate of the standard error of the proportion for the proportion that includes stock options.
  2. b. Develop an estimate of the standard error of the proportion for the proportion that includes personal use of corporate aircraft.
  3. c. Are the estimates of the standard error the same in parts (a) and (b)? If they differ, explain why.
  4. d. Develop an approximate 95% confidence interval for the proportion that includes stock options.
  5. e. Develop an approximate 95% confidence interval for the proportion that include personal use of corporate aircraft.

a.

To determine

Find an estimate of the standard error of the proportion for the proportion that includes stock options.

Explanation

Calculation:

In a study, out of 350 large U.S. companies 70% said that they did when they were asked if the companies included stock options in their CEO compensation packages and 63% said that they did when they were asked if the companies provided their CEOs personal use of corporate aircraft.

Standard error of the proportion:

The estimate of the standard error for the proportion is,

sp¯=(NnN)(p¯(1p¯)n1)

Substitute (NnN) as 1 and p¯ as 0

b.

To determine

Find an estimate of the standard error of the proportion for the proportion that includes personal use of corporate aircraft.

c.

To determine

Explain whether the estimates of the standard error in parts (a) and (b) are same or not.

d.

To determine

Obtain a 95% confidence interval for the population proportion that includes stock options.

e.

To determine

Obtain a 95% confidence interval for the population proportion that includes personal use of corporate aircraft.

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