Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. 19, X₁ =19, $₁ = 2.== 27, x₂ = 16, s₂ = 0.5.Sample 1: n₁ =Sample 2: 1₂(a) The test statistic is(b) Find the t critical value for a significance level of 0.02 for an alternative hypothesis that the first population has a larger mean (one-sided test). Use the more conservative estimate for the number of degrees of freedom: t* =(c) The conclusion isA. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and accept that the firstpopulation has a larger mean.OB. There is not sufficient evidence to warrant rejection of the claim that the two populations have the same mean.

Answered: Sample 1: n₁ = 19, x₁ = 19, s₁ = 2.…

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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Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples.

19, X₁ =
19, $₁ = 2.
=
= 27, x₂ = 16, s₂ = 0.5.
Sample 1: n₁ =
Sample 2: 1₂
(a) The test statistic is
(b) Find the t critical value for a significance level of 0.02 for an alternative hypothesis that the first population has a larger mean (one-
sided test). Use the more conservative estimate for the number of degrees of freedom: t* =
(c) The conclusion is
A. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and accept that the first
population has a larger mean.
OB. There is not sufficient evidence to warrant rejection of the claim that the two populations have the same mean.

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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