Drug Trial ProblemClinical trials for a drug was conducted using a treatment group and a placebo group. The results are shown in the table below. TreatmentPlaceboμμ₁μ₂n3338x̄2.312.65s0.950.67Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean.State the claim, null, and alternative hypothesis.Claim:μ1 μ2HO:μ1 μ2H1:μ1 μ2

Given : Claim : The two samples are from populations with the same mean. Solution : Claim : The two samples are from populations with the same mean. Let μ1 be the population mean of the treatment group and μ2 be the population mean of the placebo group. Claim : μ1 = μ2 Hypothesis test : The null and alternative hypothesis is Ho : μ1 = μ2 H1 : μ1 ≠ μ2

Answered: Drug Trial Problem Clinical trials for…

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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Drug Trial Problem
Clinical trials for a drug was conducted using a treatment group and a placebo group. The results are shown in the table below.

	Treatment	Placebo
μ	μ₁	μ₂
n	33	38
x̄	2.31	2.65
s	0.95	0.67

Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean.

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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