4th Edition

ISBN: 9780321826275

Author: Richard D. De Veaux

Publisher: PEARSON

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Chapter 15, Problem 42E

CEO compensation The total compensation of the chief executive officers (CEOs) of the 800 largest U.S. companies (the Fortune 800) averaged (in thousands of dollars) 10,307.31 with a standard deviation (also in $1000) of 17,964.62. Here is a histogram of their annual compensations (in $1000):

Chapter 15, Problem 42E, CEO compensation The total compensation of the chief executive officers (CEOs) of the 800 largest , example 1

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.

Chapter 15, Problem 42E, CEO compensation The total compensation of the chief executive officers (CEOs) of the 800 largest , example 2

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.”

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 15, Problem 41E

Chapter 15, Problem 43E

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Chapter 15 Solutions

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Solution Summary: The author analyzes how the compensation distribution of CEOs is unimodal but right-skewed, and more than one outlier is present in the data.

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