Answered: For this series of questions, you will…

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

200) For this series of questions, you will conduct an F test and a two-tailed t-test on samples from the following data sets:

Set A: 15 , 17 , 18 , 19 , 20 , 20 , 24

Set B: 19 , 18 , 18 , 17 , 15 , 15 , 13 , 13

a)The calculated F value for an F test of these two data sets.Based on the results of your F test, which t-tests could you do?

b)Assuming the results of your F-test allowed it, what would the calculated t value be for a heteroscedastic t-test of this data be?Assuming the results of your F-test allowed it, what would the calculated t value be for a homoscedastic t-test of this data be?

c)What is the appropriate conclusion of the appropriate t-test?

The mean of set B is significantly smaller than the mean of set B (p>0.05)

The mean of set B is significantly smaller than the mean of set B (0.04<p<0.05)

The mean of set B is significantly smaller than the mean of set B (0.02<p<0.04)

The mean of set B is significantly smaller than the mean of set B (0.01<p<0.02)

The mean of set B is significantly smaller than the mean of set B (0.001<p<0.01)

The mean of set B is significantly smaller than the mean of set B (p<0.001)

The means of the data sets are not significantly different from each other (p>0.05)

The means of the data sets are not significantly different from each other (0.04<p<0.05)

The means of the data sets are not significantly different from each other (0.02<p<0.04)

The means of the data sets are not significantly different from each other (0.01<p<0.02)

The means of the data sets are not significantly different from each other (0.001<p<0.01)

The means of the data sets are not significantly different from each other (p<0.001)

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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