Answered: The following data have the same sample…

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

The following data have the same sample means and variances that appeared in the preceding question but the sample size is increased to n = 10.

I	II	III
n = 10	n = 10	n = 10
M = 1	M = 5	M = 6	N = 30
T = 10	T = 50	T = 60	G = 120
s² = 9.00	s² = 10.00	s² = 11.00	∑X² = 890
SS = 81	SS = 90	SS = 99

Predict how the increase in sample size should affect the F-ratio for these data. Use an ANOVA to check your prediction.

Larger samples should the F-ratio.

Source	SS	df	MS	F
Between treatments
Within treatments
Total

Predict how the increase in sample size should affect the value of η² for these data compared to the η² in problem 10. Calculate η² to check your prediction.

Increasing the sample size should effect on η².

η² =

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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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