Fundamentals of Statistics (5th Edition)

5th Edition

ISBN: 9780134508306

Author: Michael Sullivan III

Publisher: PEARSON

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Textbook Question

Chapter 12.4, Problem 15AYU

CEO Performance Use the results of Problem 19 from Section 12.3 to answer the following:

a. Explain why it does not make sense to construct confidence or prediction intervals based on the least-squares regression equation.
b. Construct a 95% confidence interval for the mean stock return.

19. CEO Performance (Refer to Problem 31 in Section 4.1) The following data represent the total compensation for 12 randomly selected chief executive officers (CEOs) and it company’s stock performance in 2013.

Company	Compensation (millions of dollars)	Stock Return (%)
Navistar International	14.53	75.43
Aviv REIT	4.09	64.01
Groupon	7.11	142.07
Inland Real Estate	1.05	32.72
Equity Lifestyles Properties	1.97	10.64
Tootsie Roll Industries	3.76	30.66
Catamaran	12.06	0.77
Packaging Corp of America	7.62	69.39
Brunswick	8.47	58.69
LKQ	4.04	55.93
Abbott Laboratories	20.87	24.28
TreeHouse Foods	6.63	32.21

Source: Data from Chicago Tribune, June 1, 2014

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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Chapter 12.4, Problem 14AYU

Chapter 12.4, Problem 16AYU

Chapter 12 Solutions

Fundamentals of Statistics (5th Edition)

Ch. 12.1 - True or False: The shape of the chi-square...Ch. 12.1 - A _____ test is an inferential procedure used to...Ch. 12.1 - Suppose there are n independent trials of an...Ch. 12.1 - What are the two requirements that must be...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - Prob. 7AYU Ch. 12.1 - Prob. 8AYU Ch. 12.1 - In Problems 710, determine (a) the 2 test...Ch. 12.1 - In Problems 710, determine (a) the 2 test...

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?

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