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Name: for a sample of 9 automobiles, the mileage (in 1000s of miles) at whic
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Description: for a sample of 9 automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to 10% of their origin

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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for a sample of 9 automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to 10% of their original thickness. The results were as follows:

Car	Rear	Front
1	41.2	32.2
2	36.3	27.2
3	45.8	34.7
4	46.6	37.3
5	39.6	30.7
6	52.3	40.5
7	51.7	41.0
8	46.3	33.8
9	47.4	36.8

a)Construct a 99.8% confidence interval for the difference in mean lifetime between the front and rear brake pads. Let d represent the mileage of the rear pads minus the mileage of the front ones. Round the answers to at least two decimal places.

b)Because the confidence interval (contains/does not contain) values above 10 (in 1000s of miles), it (contradicts/does not contradict) the claim that the mean lifetime for rear brake pads is more than 10,000 miles more than the mean lifetime for front brake pads.

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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