Answered: A machine is set to produce disc plates…

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 machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, x-bar = 14.9 mm, and a standard deviation, s= 1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution.

State in symbols, the null and alternate hypotheses for this test.
State, with reasons, whether a t-test or a z-test will be appropriate.
Determine the rejection region(s) of the test.
Calculate the value of the test statistic.
State, with reason, a valid conclusion for the test.

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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