Answered: A manufacturing company wants to see if…

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

A manufacturing company wants to see if there is a significant difference in three types of plastic for a new product. They randomly sample prices for each of the three types of plastic and run an ANOVA. Use α = 0.05 to see if there is a statistically significant difference in the mean prices. Part of the computer output is shown below, fill in the missing information. Use � = 0.01.

a. State the correct null and alternative hypotheses.

b. Compute the test statistic. Fill out the entire ANOVA table. Round answers to at least 4 decimal places.

	Sample Mean	Sample Size
High-Density Polythene	38.5673	11
Low-Density Polythene	38.0473	15
Polyethylene Terephthalate	35.8375	8

Source	S.S.	df	M.S.	F
Treatment
Error			6.69797
Total	245.471038

c. What is the critical value?

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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