Answered: the life of two brands of canned tires…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 5E

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Question

the life of two brands of canned tires durability is a feature of interest to the manufacturer. Eight brand 1 tires and six brand 2 tires were tested. Customers prefer tires with high levels of life. The data below shows the life for both brands, in thousands of kilometers.

(Image)

a) Test the hypothesis of equality of variances for the life of the two tire brands. This is a two-sided (bilateral) test. Use an α = 0.05.

b) Test the hypothesis of equality of means for the life of the two tire brands. Use α = 0.05.

Which tire brands would you buy, if the price is the same?

Transcribed Image Text:Brand 1 107 109 95 120 117 96 109 114 Brand 2 139 127 125 129 124 115

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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