a) Use the above information to conduct a test of the null hypothesis that mean gasoline consumption is equal for the four types of cars. State the null and alternative hypotheses, fill out the ANOVA table, compare your F statistic to a tabled F value and state the conclusion of your test. Use a significance level of a = .05. b) The sample means and standard deviations for the gas mileage in the four groups are: Car type A B C D Mean 29.2 34. 27.8 29.5 Std Deviation 2.8 2. 1.2 1.0 Calculate a 95% confidence interval for mA, the mean miles per gallon for Car type A. c) What are the practical consequences of making a Type II error in the ANOVA test above?

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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To assess gasoline consumption for four types of cars, a researcher calculates the miles per gallon (mpg) that each car gets for six separate tanks of gasoline. Thus each type of car has six mpg values, for a total of 24 values. The sum of squares between cars (between groups) was 130, and the total sum of squares was 200. a) Use the above information to conduct a test of the null hypothesis that mean gasoline consumption is equal for the four types of cars. State the null and alternative hypotheses, fill out the ANOVA table, compare your F statistic to a tabled F value and state the conclusion of your test. Use a significance level of a = .05.

b) The sample means and standard deviations for the gas mileage in the four groups are:

Car type A B C D

Mean 29.2 34. 27.8 29.5

Std Deviation 2.8 2. 1.2 1.0

Calculate a 95% confidence interval for m_A, the mean miles per gallon for Car type A.

c) What are the practical consequences of making a Type II error in the ANOVA test above?

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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