MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the F-table.)
| | Treatments |
|---|--------------|
| | A | B | C | D |
|---|----|----|----|----|
| | -7 | -8 | -8 | -9 |
| | -13| -9 | -11| -16|
| | -16| -15| -5 | -17|
| | -4 | -9 | | -4 |
[Click here for the Excel Data File]
a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
Grand mean: [Input Box]
b. Calculate \( SSTR \) and \( MSTR \). (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
| | |
|------|----------|
| \( SSTR \) | [Input Box] |
| \( MSTR \) | [Input Box] |](https://content.bartleby.com/qna-images/question/64bd03e5-7334-4f8d-803b-703603d497fd/cab0ba44-a339-4a27-ac40-617e382ef370/52ltz96b_processed.jpeg)
Transcribed Image Text:Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the F-table.)
| | Treatments |
|---|--------------|
| | A | B | C | D |
|---|----|----|----|----|
| | -7 | -8 | -8 | -9 |
| | -13| -9 | -11| -16|
| | -16| -15| -5 | -17|
| | -4 | -9 | | -4 |
[Click here for the Excel Data File]
a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
Grand mean: [Input Box]
b. Calculate \( SSTR \) and \( MSTR \). (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
| | |
|------|----------|
| \( SSTR \) | [Input Box] |
| \( MSTR \) | [Input Box] |
![### Transcription for Educational Purposes
#### Statistical Analysis Task
**c.** Calculate SSE and MSE. *(Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)*
- **SSE**: [ ]
- **MSE**: [ ]
**d.** Specify the competing hypotheses to determine whether some differences exist between the population means.
- \( H_0: \mu_A = \mu_B = \mu_C; \, H_a: \) Not all population means are equal.
- \( H_0: \mu_A \neq \mu_B \neq \mu_C; \, H_a: \) Not all population means are equal.
- \( H_0: \mu_A \leq \mu_B \leq \mu_C; \, H_a: \) Not all population means are equal.
**e-1.** Calculate the value of the \( F(d_{f1}, d_{f2}) \) test statistic. *(Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)*
- **Test statistic**: [ ]
**e-2.** Find the \( p \)-value.
- \( p \)-value ≥ 0.10
- 0.05 < \( p \)-value < 0.10
- 0.025 ≤ \( p \)-value ≤ 0.05
- \( p \)-value < 0.01
- 0.01 ≤ \( p \)-value < 0.025
**f.** At the 5% significance level, what is the conclusion to the test?
- Do not reject \( H_0 \) since the \( p \)-value is not less than the significance level
- Reject \( H_0 \) since the \( p \)-value is less than the significance level](https://content.bartleby.com/qna-images/question/64bd03e5-7334-4f8d-803b-703603d497fd/cab0ba44-a339-4a27-ac40-617e382ef370/998uxnt_processed.jpeg)
Transcribed Image Text:### Transcription for Educational Purposes
#### Statistical Analysis Task
**c.** Calculate SSE and MSE. *(Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)*
- **SSE**: [ ]
- **MSE**: [ ]
**d.** Specify the competing hypotheses to determine whether some differences exist between the population means.
- \( H_0: \mu_A = \mu_B = \mu_C; \, H_a: \) Not all population means are equal.
- \( H_0: \mu_A \neq \mu_B \neq \mu_C; \, H_a: \) Not all population means are equal.
- \( H_0: \mu_A \leq \mu_B \leq \mu_C; \, H_a: \) Not all population means are equal.
**e-1.** Calculate the value of the \( F(d_{f1}, d_{f2}) \) test statistic. *(Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)*
- **Test statistic**: [ ]
**e-2.** Find the \( p \)-value.
- \( p \)-value ≥ 0.10
- 0.05 < \( p \)-value < 0.10
- 0.025 ≤ \( p \)-value ≤ 0.05
- \( p \)-value < 0.01
- 0.01 ≤ \( p \)-value < 0.025
**f.** At the 5% significance level, what is the conclusion to the test?
- Do not reject \( H_0 \) since the \( p \)-value is not less than the significance level
- Reject \( H_0 \) since the \( p \)-value is less than the significance level
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