Answered: A researcher hypothesizes that…

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 hypothesizes that different colors of cars result in different average speeds. To test this claim, she took a random sample of 20 people who own 4 different colors of colors of cars (n = 20, N = 80, G = 4), and she then tracks their average speed on the highway for a week of driving. The following ANOVA table has some of her results.
Please help her answer her research questions by completing the following ANOVA table below and answering the follow-up questions. Be sure to label your answers with the appropriate letter and show all your work!

Source	Sums of Squares	df	Mean Square	F
Effect (between)
Error (within)	100.90			------
Total	170.10		-------	------

a) What is the Sums of Squares (SS) between (effect)?

b) What are the Mean Square (MS) between (effect) and the MS within (error)?

c) What are the degrees of freedom (df) between, the df within, and the df total?

d) What is the overall F-statistic?

e) Based on the observed F-statistic (α = 0.05) and a critical F = 2.47, should she retain or reject the null hypothesis?

f) In everyday language, what can she conclude about the research question?

Suppose that the average speed for Red Cars was 72.5 and the average speed for White Cars was 68.2.

a) Calculate and report (including the degrees of freedom) a follow-up t-test using an α (alpha) = 0.05 and a critical t = 1.98.

b) In everyday language, what can she conclude about how people who drive red versus white cars?

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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