Following is the total compensation, in millions of dollars, for Chief Executive Officers (CEOs) at 20 large U.S. corporations in a recent year.2.75 9.15 2.32 23.84 13.12 9.91 6.39 2.19 4.28 0.703.18 8.20 1.68 4.64 6.05 6.59 11.31 1.35 25.84 2.85A research firm would like to analyze the mean compensation of CEOs in the U.S. and has decided to construct a 99% confidence interval to estimate the mean compensation amount.Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.Is it reasonable to assume that this sample came from a normal population? Explain.If appropriate, construct a 99% confidence interval for the mean compensation of a CEO in the U.S. using Excel procedures similar to those used in the previous problems. If it is not appropriate to construct the confidence interval, then explain why it is not appropriate.

Answered: Following is the total compensation, in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Following is the total compensation, in millions of dollars, for Chief Executive Officers (CEOs) at 20 large U.S. corporations in a recent year.

2.75 9.15 2.32 23.84 13.12 9.91 6.39 2.19 4.28 0.70

3.18 8.20 1.68 4.64 6.05 6.59 11.31 1.35 25.84 2.85

A research firm would like to analyze the mean compensation of CEOs in the U.S. and has decided to construct a 99% confidence interval to estimate the mean compensation amount.

Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.
Is it reasonable to assume that this sample came from a normal population? Explain.
If appropriate, construct a 99% confidence interval for the mean compensation of a CEO in the U.S. using Excel procedures similar to those used in the previous problems. If it is not appropriate to construct the confidence interval, then explain why it is not appropriate.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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