6.13 A firm has a generous but rather complicated policy concerning end-of-year bonuses for its lower-level managerial personnel. The policy’s key factor is a subjective judgment of “contribu- tion to corporate goals.” A personnel officer took samples of 24 female and 36 male managers to see whether there was any difference in bonuses, expressed as a percentage of yearly salary. The data are listed here: Gender Bonus Percentage F 9.2 7.7 11.9 6.2 9.0 8.4 6.9 7.6 7.4 F 8.0 9.9 6.7 8.4 9.3 9.1 8.7 9.2 9.1 F 8.4 9.6 7.7 9.0 9.0 8.4 M 10.4 8.9 11.7 12.0 8.7 9.4 9.8 9.0 9.2 M 9.7 9.1 8.8 7.9 9.9 10.0 10.1 9.0 11.4 M 8.7 9.6 9.2 9.7 8.9 9.2 9.4 9.7 8.9 M 9.3 10.4 11.9 9.0 12.0 9.6 9.2 9.9 9.0 a. What are the populations of interest in this study? b. Is there significant evidence that the mean bonus percentage for males is more than five units larger than the mean bonus percentage for females? Use a 5 .05. c. What is the level of significance of your test? d. Estimate the difference in the mean bonus percentages for males and females using a 95% confidence interval.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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6.13

A firm has a generous but rather complicated policy concerning end-of-year bonuses for its lower-level managerial personnel. The policy’s key factor is a subjective judgment of “contribu- tion to corporate goals.” A personnel officer took samples of 24 female and 36 male managers to see whether there was any difference in bonuses, expressed as a percentage of yearly salary. The data are listed here:

Gender Bonus Percentage

F 9.2 7.7 11.9 6.2 9.0 8.4 6.9 7.6 7.4

F 8.0 9.9 6.7 8.4 9.3 9.1 8.7 9.2 9.1

F 8.4 9.6 7.7 9.0 9.0 8.4

M 10.4 8.9 11.7 12.0 8.7 9.4 9.8 9.0 9.2

M 9.7 9.1 8.8 7.9 9.9 10.0 10.1 9.0 11.4

M 8.7 9.6 9.2 9.7 8.9 9.2 9.4 9.7 8.9

M 9.3 10.4 11.9 9.0 12.0 9.6 9.2 9.9 9.0

a. What are the populations of interest in this study?

b. Is there significant evidence that the mean bonus percentage for males is more than five units larger than the mean bonus percentage for females? Use a 5 .05.

c. What is the level of significance of your test?

d. Estimate the difference in the mean bonus percentages for males and females using a 95% confidence interval.

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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