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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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
Ha: μ1 = μ2 = μ3
2. H0: Not all the population means are equal.
Ha: μ1 = μ2 = μ3
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.
Ha: At least two of the population means are different.
4. H0: μ1 = μ2 = μ3
Ha: μ1 ≠ μ2 ≠ μ3
Ha: μ1 ≠ μ2 ≠ μ3
5. H0: μ1 = μ2 = μ3
Ha: Not all the population means are equal.
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.
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