To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, a chemical company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 20 28 21 25 27 20 25 30 22 26 31 25 (a) Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use ? = 0.05. State the null and alternative hypotheses. 1. H0: μ1 ≠ μ2 ≠ μ3 Ha: μ1 = μ2 = μ3 2. H0: Not all the population means are equal. Ha: μ1 = μ2 = μ3 3. H0: At least two of the population means are equal. Ha: At least two of the population means are different. 4. H0: μ1 = μ2 = μ3 Ha: μ1 ≠ μ2 ≠ μ3 5. H0: μ1 = μ2 = μ3 Ha: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) ( ) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. 1. Reject H0. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. 2. Do not reject H0. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. 3. Do not reject H0. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. 4. Reject H0. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. (b) At the ? = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. Find the value of LSD. (Round your answer to two decimal places.) LSD = ( ) Find the pairwise absolute difference between sample means for manufacturers 1 and 3. /x1 − x3/= What conclusion can you draw after carrying out this test? 1. There is a significant difference between the means for manufacturer 1 and manufacturer 3. 2. There is not a significant difference between the means for manufacturer 1 and manufacturer 3

To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, a chemical company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 20 28 21 25 27 20 25 30 22 26 31 25 (a) Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use ? = 0.05. State the null and alternative hypotheses. 1. H0: μ1 ≠ μ2 ≠ μ3 Ha: μ1 = μ2 = μ3 2. H0: Not all the population means are equal. Ha: μ1 = μ2 = μ3 3. H0: At least two of the population means are equal. Ha: At least two of the population means are different. 4. H0: μ1 = μ2 = μ3 Ha: μ1 ≠ μ2 ≠ μ3 5. H0: μ1 = μ2 = μ3 Ha: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) ( ) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. 1. Reject H0. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. 2. Do not reject H0. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. 3. Do not reject H0. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. 4. Reject H0. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. (b) At the ? = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. Find the value of LSD. (Round your answer to two decimal places.) LSD = ( ) Find the pairwise absolute difference between sample means for manufacturers 1 and 3. /x1 − x3/= What conclusion can you draw after carrying out this test? 1. There is a significant difference between the means for manufacturer 1 and manufacturer 3. 2. There is not a significant difference between the means for manufacturer 1 and manufacturer 3

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

Manufacturer
1	2	3
20	28	21
25	27	20
25	30	22
26	31	25

(a)

Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use

? = 0.05.

State the null and alternative hypotheses.

1. H₀: μ₁ ≠ μ₂ ≠ μ₃
H_a: μ₁ = μ₂ = μ₃

2. H₀: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃

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

4. H₀: μ₁ = μ₂ = μ₃
H_a: μ₁ ≠ μ₂ ≠ μ₃

5. H₀: μ₁ = μ₂ = μ₃
H_a: Not all the population means are equal.

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

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

p-value =

State your conclusion.

1. Reject H₀. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.

2. Do not reject H₀. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.

3. Do not reject H₀. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.

4. Reject H₀. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.

(b)

At the ? = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3.

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

LSD = ( )

Find the pairwise absolute difference between sample means for manufacturers 1 and 3.

/x₁ − x_3/=

What conclusion can you draw after carrying out this test?

1. There is a significant difference between the means for manufacturer 1 and manufacturer 3.

2. There is not a significant difference between the means for manufacturer 1 and manufacturer 3.

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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