Answered: Problem The amount of shaft wear…

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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The amount of shaft wear (measured in inches) after a fixed mileage was determined for each of n =8 internal combustion engines having copper lead as a bearing material, with ̄x =3.72 X 10^-4and s =1.25 X 10^-4. The quality control department wants to know if any evidence exists to suggest that the true mean shaft wear U is greater than 3.5 X 10^-4 inches.

(a) Set up the null and alternative hypotheses.

(b) Give a Type 1 and Type 2 error in context of this problem.

(c) Conduct the hypothesis test at a =0.05. Clearly specify the distribution used, critical value, test statistic, and decision in context of the problem.

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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