A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 8 of their tires and has provided the following data.Life Expectancy(In Thousands of Miles)2827252628262925a.Determine the mean and the standard deviation.b.Formulate the correct hypotheses to determine whether or not the tire company is using legitimate adversiting. c.At the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.d.Repeat the test using the p-value approach.

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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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A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 8 of their tires and has provided the following data.

Life Expectancy
(In Thousands of Miles)
28
27
25
26
28
26
29
25

a.	Determine the mean and the standard deviation.
b.	Formulate the correct hypotheses to determine whether or not the tire company is using legitimate adversiting.
c.	At the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.
d.	Repeat the test using the p-value approach.

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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