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.

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