To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material. 1 2 17 28 23 26 21 31 19 27 a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use α = 0.05. Compute the values below (to 2 decimals, if necessary). Sum of Squares, Treatment Sum of Squares, Error Mean Squares, Treatment Mean Squares, Error Calculate the value of the test statistic (to 2 decimals). Manufacturer What conclusion can you draw after carrying out this test? - Select your answer - 3 18 17 21 20 The p-value is - Select your answer - + What is your conclusion? - Select your answer - b. At the a = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. Calculate Fisher's LSD Value (to 2 decimals).
To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material. 1 2 17 28 23 26 21 31 19 27 a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use α = 0.05. Compute the values below (to 2 decimals, if necessary). Sum of Squares, Treatment Sum of Squares, Error Mean Squares, Treatment Mean Squares, Error Calculate the value of the test statistic (to 2 decimals). Manufacturer What conclusion can you draw after carrying out this test? - Select your answer - 3 18 17 21 20 The p-value is - Select your answer - + What is your conclusion? - Select your answer - b. At the a = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. Calculate Fisher's LSD Value (to 2 decimals).
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Testing the Mean Time for Mixing Material by Manufacturer
To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material.
#### Mixing Time Data (in minutes)
| Manufacturer | 1 | 2 | 3 |
|--------------|----|----|----|
| **Mixing Times** | 17 | 28 | 18 |
| | 23 | 26 | 17 |
| | 21 | 31 | 21 |
| | 19 | 27 | 20 |
### a. Hypothesis Testing
**Task:** Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use significance level \(\alpha = 0.05\).
**Steps:**
1. Compute the following values (to 2 decimal places, if necessary):
- Sum of Squares, Treatment (SST)
- Sum of Squares, Error (SSE)
- Mean Squares, Treatment (MST)
- Mean Squares, Error (MSE)
2. Calculate the value of the test statistic (to 2 decimals).
3. The p-value is:
- [Select your answer]
4. What is your conclusion?
- [Select your answer]
**Calculations:**
- **Sum of Squares, Treatment:** \[\text{SST} = \]
- **Sum of Squares, Error:** \[\text{SSE} = \]
- **Mean Squares, Treatment:** \[\text{MST} = \]
- **Mean Squares, Error:** \[\text{MSE} = \]
- **Test Statistic:** \[\text{Calculated Value} = \]
### b. Fisher's LSD Test
1. At \(\alpha = 0.05\) level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3.
2. Calculate Fisher’s LSD Value (to 2 decimals).
**Fisher’s LSD Value:** \[\text{LSD} = \]
3. What conclusion can you draw after carrying out this test?
- [Select your answer]
**Conclusion:**
- Based on the calculations and applied tests, conclude if the mean times for mixing material significantly differ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8514667-bf86-4079-a5fb-967fac7b38d7%2Ff0e61387-4eaa-4d56-8a87-6dc01e77e43c%2Fsy03lw_processed.png&w=3840&q=75)
Transcribed Image Text:### Testing the Mean Time for Mixing Material by Manufacturer
To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material.
#### Mixing Time Data (in minutes)
| Manufacturer | 1 | 2 | 3 |
|--------------|----|----|----|
| **Mixing Times** | 17 | 28 | 18 |
| | 23 | 26 | 17 |
| | 21 | 31 | 21 |
| | 19 | 27 | 20 |
### a. Hypothesis Testing
**Task:** Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use significance level \(\alpha = 0.05\).
**Steps:**
1. Compute the following values (to 2 decimal places, if necessary):
- Sum of Squares, Treatment (SST)
- Sum of Squares, Error (SSE)
- Mean Squares, Treatment (MST)
- Mean Squares, Error (MSE)
2. Calculate the value of the test statistic (to 2 decimals).
3. The p-value is:
- [Select your answer]
4. What is your conclusion?
- [Select your answer]
**Calculations:**
- **Sum of Squares, Treatment:** \[\text{SST} = \]
- **Sum of Squares, Error:** \[\text{SSE} = \]
- **Mean Squares, Treatment:** \[\text{MST} = \]
- **Mean Squares, Error:** \[\text{MSE} = \]
- **Test Statistic:** \[\text{Calculated Value} = \]
### b. Fisher's LSD Test
1. At \(\alpha = 0.05\) level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3.
2. Calculate Fisher’s LSD Value (to 2 decimals).
**Fisher’s LSD Value:** \[\text{LSD} = \]
3. What conclusion can you draw after carrying out this test?
- [Select your answer]
**Conclusion:**
- Based on the calculations and applied tests, conclude if the mean times for mixing material significantly differ
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Step 1: State the hypotheses.
VIEWStep 2: Obtain the values in ANOVA table.
VIEWStep 3: The conclusion is obtained as follows:
VIEWStep 4: Obtain the fisher’s LSD value for the equality of means between manufacturers 1 and 3.
VIEWStep 5: Determine whether the test for the equality of the means for manufacturers 1 and 3.
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