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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

We want to know if the average rating of attractiveness (1=homely, 5=stunning) of a typical person differs depending on the state they are located in. We believe that there will be significant differences in the average attractiveness of the people at each of the four states we examine.

1) Report (in words or statistical notation), our null and alternative hypothesis:

Provided are the data we collected from four different states: OR, WA, ID, and CA (see below):

	OR	WA	ID	CA
X bar	3.01	3.07	2.88	3.7
SD	0.42	0.60	0.46	0.30
n	10	10	10	9
SS	92.19	97.47	84.84	123.95

2) Given that we have more than two samples, we need to conduct a one-way ANOVA. Conduct the test in order to calculate the F-statistic addressing our hypothesis. Be sure to calculate the grand mean and the between-groups & within-groups mean-squares first (also don’t forget to round to 2 decimal places and report the formulas!!):

3.) Calculate the degrees of freedom (df) for this test. Given that we are setting α = .05, what is the critical value for the Fdistribution given our data set and hypothesis

4.) In words, interpret what the significance testing tells us about whether or not the samples differ on our variable of interest (describe the variable). Also, report the results in APA format:

5.)Do you believe the F-statistic a good representation of whether or not we truly had differences between groups in this specific data set? Why or why not?

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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