A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population. Moreover, the variable is normally distributed on each of the two populations. (a)For independent samples of sizes 9 and 4, respectively, determine the mean and standard deviation of ?̅ 1 − ?̅ 2 (b)Can you conclude that the variable ?̅ 1 − ?̅ 2 is normally distributed? Explain your answer (c)Determine the percentage of all pairs of independent samples of sizes 9 and 4, respectively, from the two populations with the property that the difference ?̅ 1 − ?̅ 2 between the sample means is between -10 and 10 3. A variable of two populations has a mean of 40 and a standard deviation of 12 for one of thepopulations and a mean of 40 and a standard deviation of 6 for the other population. Moreover, thevariable is normally distributed on each of the two populations.(a)For independent samples of sizes 9 and 4, respectively, determine the mean and standard deviationof X1-X 2(b)Can you conclude that the variable X1-X 2 is normally distributed? Explain your answer(c)Determine the percentage of all pairs of independent samples of sizes 9 and 4, respectively, from thetwo populations with the property that the difference X 1- X 2 between the sample means is between -10 and 10

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Description: A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population. Moreover, the variable is normally distributed on each of the two popula

a) The mean and standard deviation is given as follows: EX¯1-X¯2=EX¯1-EX¯2 =40-40…

Answered: A variable of two populations has a…

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 variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population. Moreover, the variable is normally distributed on each of the two populations.

(a)For independent samples of sizes 9 and 4, respectively, determine the mean and standard deviation of ?̅ 1 − ?̅ 2

(b)Can you conclude that the variable ?̅ 1 − ?̅ 2 is normally distributed? Explain your answer

(c)Determine the percentage of all pairs of independent samples of sizes 9 and 4, respectively, from the two populations with the property that the difference ?̅ 1 − ?̅ 2 between the sample means is between -10 and 10

3. A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the
populations and a mean of 40 and a standard deviation of 6 for the other population. Moreover, the
variable is normally distributed on each of the two populations.
(a)For independent samples of sizes 9 and 4, respectively, determine the mean and standard deviation
of X1-X 2
(b)Can you conclude that the variable X1-X 2 is normally distributed? Explain your answer
(c)Determine the percentage of all pairs of independent samples of sizes 9 and 4, respectively, from the
two populations with the property that the difference X 1- X 2 between the sample means is between -
10 and 10

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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