Answered: A researcher wishes to determine…

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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A researcher wishes to determine whether the salaries of professional nurses’
employees by private hospitals are higher than those of nurse’s employees by government-owned hospitals. She selects a sample of nurses from each type of hospital and calculates the mean and standard deviation of their salaries. At o.o1 level of significance, can she conclude that the average pay at private hospitals is more than the average pay at government hospitals? Assume that the populations are approximately normally distributed and having unknown and unequal population variances.

Private	Government
Mean= $26,800	Mean= $25,400
S₁= $600	S₂= $450
n₁=10	n₂=8

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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