Answered: A researcher wishes to see if there is…

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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Question

A researcher wishes to see if there is no difference in the fuel economy for city driving for three different types of automobiles: small automobiles, sedans, and luxury automobiles. He randomly samples 4 small automobiles, 5 sedans, and 3 luxury automobiles. The miles per gallon for each is shown. At α = 0.05 ,use the analysis of variance test to test the claim that there is no difference among the means.

Small	Sedan	Luxury
35	42	28
43	37	26
32	33	23
37	27
	39

a. State the hypothesis:

b. Find the critical value(s). (Draw a bell curve, label your mean and shade the area that you are trying to find and Round the nearest hundredths)

c. Compute the test statistic. (Round the nearest thousandths)

* Find the mean and variance of each sample. (Round the nearest thousandths)

*Find the Grand Mean. (Round the nearest thousandths)

*Find the between-group variance. (Round the nearest thousandths)

* Find the with-in group variance. (Round the nearest thousandths)

* Find the F-test value. (Round the nearest hundredths)

d. Make a decision.

e. Summarize your conclusion in a COMPLETE SENTENCE.

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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