Answered: To test for any significant difference…

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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To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.

Machine 1	Machine 2	Machine 3	Machine 4
6.6	8.8	10.9	9.5
7.9	7.3	10.0	12.5
5.5	9.3	9.3	11.9
7.6	10.2	10.0	10.6
8.5	9.2	8.8	11.1
7.1	9.8	8.6	11.0

(a)

At the ? = 0.05 level of significance, what is the difference, if any, in the population mean times among the four machines?

State the null and alternative hypotheses.

-H₀: Not all the population means are equal.
H_a: ?₁ = ?₂ = ?₃ = ?₄

-H₀: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄
H_a: ?₁ = ?₂ = ?₃ = ?₄

-H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

-H₀: ?₁ = ?₂ = ?₃ = ?₄
H_a: Not all the population means are equal.

-H₀: ?₁ = ?₂ = ?₃ = ?₄
H_a: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

Find the p-value. (Round your answer to three decimal places.)

p-value = ??

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.

Reject H₀. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.

Do not reject H₀. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.

Reject H₀. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.

(b)

Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a 0.05 level of significance.

Find the value of LSD. (Round your answer to two decimal places.)

LSD = ??

Find the pairwise absolute difference between sample means for machines 2 and 4.

x₂ − x_4=??

What conclusion can you draw after carrying out this test?

There is a significant difference between the means for machines 2 and 4.There is not a significant difference between the means for machines 2 and 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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