Answered: 2. A valve manufacturer produces a…

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

2. A valve manufacturer produces a butterfly valve composed of two
semicircular plates on a common spindle that is used to permit flow in
one direction only. The semicircular plates are supplied by a vendor with
specifications that the plates be 2.37 millimeters thick and have a tensile
strength of five pounds per millimeter. A random sample of 20 such
plates is taken. Electronic calipers are used to measure the thickness of
each plate. A universal testing machine was used to test the tensile
strength. The sample data are found Below.

a. Determine, with 95% confidence, if mean tensile strength is less than five pounds per
millimeter. Use the critical value approach.
b. Are more than half of plates thicker than 2.37? Use the p-value approach with 95%
confidence.

Thickness	Strength
2.4066	4.9175
2.1328	4.8067
2.5937	5.1246
2.1933	4.7555
2.4579	4.7233
2.0665	4.3934
2.1994	4.4609
2.4575	4.7377
2.6724	4.3407
2.2738	4.9487
2.5392	4.4265
2.7956	4.3583
2.1228	4.5608
2.2055	4.8207
2.4359	4.7769
2.3353	5.2468
2.3238	4.8706
2.5267	4.5138
2.2146	4.4402
2.2699	4.6548

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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