Based on the following values: Mathematical expectation: E(X) = ∑Xn1 = 1204 = 30E(Y) = ∑Yn2 = 1884 = 47E(Z) = ∑Zn3 = 1784 = 44.5Variance: var(X) = 1n1-1∑X2-1n∑X2 = 14-13678-12024 =26var(Y) = 1n2-1∑Y2-1n∑Y2 = 14-18890-18824 =18var(Z) = 1n3-1∑Z2-1n3∑Z2 = 14-18322-17824 =133.6667Root mean square deviationsd(X)= var(X) =26 = 5.0990sd(Y)= var(Y) =18 = 4.2426sd(Z)= var(Z) =133.6667 = 11.5614Correlation coefficientsXYZ 254428 284348 374955 3052471. Expectation1201881782. Variance2618133.66673. root mean square deviation5.0994.242611.5614 Check the hypothesis in the images. The table values are in the other image below α = 0.05T(a/2, v = 2) = 4.3027T(a/2, v = 3) = 3.1825T(a/2, v = 4): = 2.7765T(a/2, v = 6) = 2.4469F(a/2, 4, 4) = 9.6045F(a/2,3,3) = 15.4392F(α/2,3,4)= 9.9792F(a/2, 1,4)= 7.708F(a/2,4,3)= 9.12G(a, 3, 3) = = 0.7977x² = x²(₁3) =x² = x² (1-2, 3) = = 9.348T(α, 4) = 1.71= 0.2158 Check the following hypotheses:1) Verification of hypothesis variancesHo: o2 = 0; H₁:02 #0²2) Verification of hypothesis variancesHo: o² = 0²; H₁: 0} # 0²3) Verification of hypothesis variancesHo: o2 = 0; H₁: 0² # 0²

The standard deviation of the two samples is compared using the F test. It tests the variance of…

Answered: Check the following hypotheses: 1)…

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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Question

Based on the following values:

Mathematical expectation:

E(X) = ∑Xn1 = 1204 = 30

E(Y) = ∑Yn2 = 1884 = 47

E(Z) = ∑Zn3 = 1784 = 44.5

Variance:

var(X) = 1n1-1∑X2-1n∑X2 = 14-13678-12024 =26

var(Y) = 1n2-1∑Y2-1n∑Y2 = 14-18890-18824 =18

var(Z) = 1n3-1∑Z2-1n3∑Z2 = 14-18322-17824 =133.6667

Root mean square deviation

sd(X)= var(X) =26 = 5.0990

sd(Y)= var(Y) =18 = 4.2426

sd(Z)= var(Z) =133.6667 = 11.5614

Correlation coefficients

X	Y	Z
	25	44	28
	28	43	48
	37	49	55
	30	52	47
1. Expectation	*120*	*188*	*178*
2. Variance	26	18	*133.6667*
3. root mean square deviation	*5.099*	*4.2426*	*11.5614*

Check the hypothesis in the images. The table values are in the other image below

α = 0.05
T(a/2, v = 2) = 4.3027
T(a/2, v = 3) = 3.1825
T(a/2, v = 4): = 2.7765
T(a/2, v = 6) = 2.4469
F(a/2, 4, 4) = 9.6045
F(a/2,3,3) = 15.4392
F(α/2,3,4)= 9.9792
F(a/2, 1,4)= 7.708
F(a/2,4,3)= 9.12
G(a, 3, 3) = = 0.7977
x² = x²(₁3) =
x² = x² (1-2, 3) = = 9.348
T(α, 4) = 1.71
= 0.2158

Check the following hypotheses:
1) Verification of hypothesis variances
Ho: o2 = 0; H₁:02 #0²
2) Verification of hypothesis variances
Ho: o² = 0²; H₁: 0} # 0²
3) Verification of hypothesis variances
Ho: o2 = 0; H₁: 0² # 0²

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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