Magnet ProblemResearchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table below. The results are a measure of reduction in back pain. Assume that the two samples are independent random samples. TreatmentShamμμ₁μ₂n1818x̄0.570.42s0.541.46Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.State the claim, null, and alternative hypothesis.Claim:μ1 μ2HO:μ1 μ2H1:μ1 μ2

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Answered: Researchers conducted a study to…

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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Magnet Problem
Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table below. The results are a measure of reduction in back pain. Assume that the two samples are independent random samples.

	Treatment	Sham
μ	μ₁	μ₂
n	18	18
x̄	0.57	0.42
s	0.54	1.46

Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

State the claim, null, and alternative hypothesis.

Claim:	_μ1	_μ2
H_O:	_μ1	_μ2
H₁:	_μ1	_μ2

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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