Answered: 3. Two machines are used for filling…

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

Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed normal, with standard deviation σ1 = 0.020 and σ2 = 0.025 ounces. A member of the quality engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine.

Please show detailed solution. Please answer letter a-e

3.
Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be
assumed normal, with standard deviation o1 = 0.020 and o2 = 0.025 ounces. A member of the quality
engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume
is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine.
MACHINE 1
MACHINE 2
16.03
16.01
16.02
16.03
16.04
15.96
15.97
16.04
16.05
15.98
15.96
16.02
16.05
16.02
16.01
16.01
16.02
15.99
15.99
16.00
(a) Do you think the engineer is correct? Use a = 0.05.
(b) What is the P-value for this test?
(c) What is the power of the test in part (a) for a true difference in means of 0.04?
(d) Find a 95% confidence interval on the difference in means. Provide a practical interpretation of
this interval.
(e) Assuming equal sample sizes, what sample size should be used to assure that B = 0.05 if the
true difference in means is 0.04? Assume that a = 0.05.

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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