Answered: In quality–control applications of…

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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Question

In quality–control

applications of hypothesis testing, the null and alternative hypotheses are frequently specified as

H0:

The production process is performing satisfactorily and

Ha:

The process is performing in an unsatisfactory manner. Accordingly,

is sometimes referred to as the producer's risk, while

is called the consumer's risk. An injection molder produces plastic golf tees with a mean weight of

0.252

ounce. To investigate whether the injection molder is operating satisfactorily,

tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the accompanying table

Write

and

in terms of the true mean weight of the golf tees,

μ.

H0:

μ=0.252

Ha:

μ<0.252

H0:

μ=0.252

Ha:

μ≠0.252

H0:

μ=0.252

Ha:

μ>0.252

H0:

μ≠0.252

Ha:

μ=

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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