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Category > Business & Finance Posted 07 May 2017 My Price 8.00

According to the Central Limit Theorem

 

CEOs revisited. In Exercise 30 you looked at the annual compensation for 800 CEOs, for which the true mean and standard deviation were (in thousands of dollars) 10,307.31 and 17,964.62, respectively. A simulation drew samples of sizes 30, 50, 100, and 200 (with replacement) from the total annual compensations of the Fortune 800 CEOs. The summary statistics for these simulations were as follows:

a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes?

b) How close are the theoretical values to what was observed from the simulation?

c) Looking at the histograms in Exercise 30, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?

d) What about the shape of the distribution of Total Compensation explains your answer in part c?

Exercise 30:

CEO compensation. In Chapter 4 we saw the distribution of the total compensation of the chief executive officers (CEOs) of the 800 largest U.S. companies (the Fortune 800). The average compensation (in thousands of dollars) is 10,307.31 and the standard deviation is 17,964.62. Here is a histogram of their annual compensations (in $1000):

a) Describe the histogram of Total Compensation. A research organization simulated sample means by drawing samples of 30, 50, 100, and 200, with replacement, from the 800 CEOs. The histograms show the distributions of means for many samples of each size.

b) Explain how these histograms demonstrate what the Central Limit Theorem says about the sampling distribution model for sample means. Be sure to talk about shape, center, and spread.

c) Comment on the rule of thumb that With a sample size of at least 30, the sampling distribution of the mean is Normal?

 

 

 
 

Answers

Alpha Geek
(8)
Status NEW Posted 07 May 2017 09:05 AM My Price 8.00

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file 1494150796-Answer.docx preview (326 words )
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