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Solved: Executive Compensation Scoreboard. Refer to
Chapter 6, Problem 17E(choose chapter or problem)
Executive Compensation Scoreboard. Refer to Forbes’ 2011 “Executive Compensation Scoreboard.” Recall that the data file contains the 2011 salaries (in $ millions) of the 500 CEOs that participated in the Forbes’ survey. Suppose you are interested in estimating the mean 2011 salary for these 500 CEOs.
a. What is the target parameter?
b. Obtain a random sample of 50 salaries from the data set.
c. Find the mean of the 50 salaries, part b.
d. Verify that the standard deviation for the population of 500 salaries is \(\sigma=\$ 9.84 \text { million. }\)
e. Use the information, parts c and d, to form a 99% confidence interval for the true mean 2011 salary of the 500 CEOs in the Forbes’ survey.
f. Give a practical interpretation of the interval, part e.
g. Find the true mean salary of the 500 CEOs and check to see if this value falls within the 99% confidence interval, part e.
Questions & Answers
QUESTION:
Executive Compensation Scoreboard. Refer to Forbes’ 2011 “Executive Compensation Scoreboard.” Recall that the data file contains the 2011 salaries (in $ millions) of the 500 CEOs that participated in the Forbes’ survey. Suppose you are interested in estimating the mean 2011 salary for these 500 CEOs.
a. What is the target parameter?
b. Obtain a random sample of 50 salaries from the data set.
c. Find the mean of the 50 salaries, part b.
d. Verify that the standard deviation for the population of 500 salaries is \(\sigma=\$ 9.84 \text { million. }\)
e. Use the information, parts c and d, to form a 99% confidence interval for the true mean 2011 salary of the 500 CEOs in the Forbes’ survey.
f. Give a practical interpretation of the interval, part e.
g. Find the true mean salary of the 500 CEOs and check to see if this value falls within the 99% confidence interval, part e.
ANSWER:Step 1 of 7
(a)
The average of the 2011 salaries of the 500 CEOs that participated in the Forbes survey is considered as the target parameter \(\mu\).
\(\mu \) = mean salary of all 500 CEOs