Answered: In Case Study 9.1, we discussed the…

Name: In Case Study 9.1, we discussed the National Survey for Professional,
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Description: In Case Study 9.1, we discussed the National Survey for Professional, Administrative, Technical, and Clerical Pay, which is conducted annually to determine whether federal pay scales are commensurate with private sector salaries. Recall that governm

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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In Case Study 9.1, we discussed the National Survey for Professional, Administrative, Technical, and Clerical Pay, which is conducted annually to determine whether federal pay scales are commensurate with private sector salaries. Recall that government and private workers in the study are matched as closely as possible before the salaries are compared. Suppose that the table shows the annual salaries for twelve pairs of individuals in the sample matched on job level and experience. Use these data to construct a 99% confidence interval for the difference between the mean salaries of the private and government sectors.

PAIR	PRIVATE	GOV’T	PAIR	PRIVATE	GOV’T
1	$12,500	$11,700	7	$15,800	$14,500
2	22,300	20,900	8	17,500	17,900
3	14,500	14,800	9	23,300	21,400
4	32,300	29,900	10	42,100	43,200
5	20,800	21,500	11	16,800	15,200
6	19,200	18,400	12	14,500	14,200

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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