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Description: A sample of 77 measurments, randomly selected from a normally distributed population, resulted in a sample mean x¯=8.9 and sample standard deviation ?=1.92. Using ?=0.01, test the null hypothesis that the mean of the population is 8.4 against the alt

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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A sample of 77 measurments, randomly selected from a normally distributed population, resulted in a sample mean x¯=8.9 and sample standard deviation ?=1.92. Using ?=0.01, test the null hypothesis that the mean of the population is 8.4 against the alternative hypothesis that the mean of the population is less than 8.4 by giving the following:
(a)    the degree of freedom :
(b)    the critical ? value :
(c)    the test statistic :

The final conclusion is

A. We can reject the null hypothesis that ?=8.4.
B. There is not sufficient evidence to reject the null hypothesis that ?=8.4.

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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