Answered: Refer to Exercise 1 in Section 9.1. 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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Refer to Exercise 1 in Section 9.1. A scientist wants to determine whether the mean strength
of specimens cured at 30°C differs from the mean strengths of specimens cured at 0°C,
10°C, and 20°C.
a) Use the Bonferroni method to determine which of the means, if any, for 0°C, 10°C,
and 20°C differ from the mean for 30°C. Use the 5% level.
b) Use the Tukey–Kramer method to determine which of the means, if any, 0°C, 10°C,
and 20°C differ from the mean for 30°C. Use the 5% level.
c) Which is the more powerful method to find all the treatments whose means differ from
that of the 30°C temperature, the Bonferroni method or the Tukey–Kramer method?

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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