You may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. In the following calculations, use α = 0.05. Treatment 1 63 46 53 46 52 64.67 Treatment 2 Ho: H₁ H₂ H3 На: Н1 =H2 =Из 83 71 87 OH ₁: M₁₂ = H₂ = μ3 на: H1 #Hz #Из 71 78 68.00 Treatment 3 70 54 61 51 O Ho: Not all the population means are equal. H₂H₁ = H₂=H3 (a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses. 59 71.33 H₁²H₁₂ = H₂=H3 H₂: Not all the population means are equal. O Ho: At least two of the population means are equal. H₂: At least two of the population means are different. Find the value of the test statistic. (Round your answer to two decimal places.) X Find the p-value. (Round your answer to three decimal places.) p-value = x State your conclusion. O Reject Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. ● Reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal. Do not reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal.
You may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. In the following calculations, use α = 0.05. Treatment 1 63 46 53 46 52 64.67 Treatment 2 Ho: H₁ H₂ H3 На: Н1 =H2 =Из 83 71 87 OH ₁: M₁₂ = H₂ = μ3 на: H1 #Hz #Из 71 78 68.00 Treatment 3 70 54 61 51 O Ho: Not all the population means are equal. H₂H₁ = H₂=H3 (a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses. 59 71.33 H₁²H₁₂ = H₂=H3 H₂: Not all the population means are equal. O Ho: At least two of the population means are equal. H₂: At least two of the population means are different. Find the value of the test statistic. (Round your answer to two decimal places.) X Find the p-value. (Round your answer to three decimal places.) p-value = x State your conclusion. O Reject Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means of the three treatments are not equal. ● Reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal. Do not reject Ho. There is sufficient evidence to conclude that the means of the three treatments are not equal.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Analysis of Variance (ANOVA) Test
You may need to use appropriate technology to answer this question.
The following data are from a completely randomized design. In the following calculations, use α = 0.05.
#### Data:
| | Treatment 1 | Treatment 2 | Treatment 3 |
|------------|-------------|-------------|-------------|
| Values | 63 | 83 | 70 |
| | 46 | 71 | 54 |
| | 53 | 87 | 61 |
| | 46 | 71 | 51 |
| Mean (\( \bar{x}_j \)) | 52 | 78 | 59 |
| Variance (\( s_j^2 \)) | 64.67 | 68.00 | 71.33 |
#### (a) Use analysis of variance to test for a significant difference among the means of the three treatments.
**State the null and alternative hypotheses.**
- **Correct Choice:**
- \( H_0: \mu_1 = \mu_2 = \mu_3 \)
- \( H_a: \) Not all the population means are equal.
**Find the value of the test statistic.**
- (Round your answer to two decimal places.)
- [Input box not filled, marked as incorrect]
**Find the p-value.**
- (Round your answer to three decimal places.)
- p-value = [Input box not filled, marked as incorrect]
**State your conclusion.**
- **Correct Option:**
- Reject \( H_0 \). There is sufficient evidence to conclude that the means of the three treatments are not equal.
This exercise involves using ANOVA to determine if there are any statistically significant differences between the means of the treatments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6886f08-90b0-4bd9-a192-6e28f2935ee7%2Fa149accf-ccd5-4c6c-bf3e-96ab677cc711%2Ffze288b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Variance (ANOVA) Test
You may need to use appropriate technology to answer this question.
The following data are from a completely randomized design. In the following calculations, use α = 0.05.
#### Data:
| | Treatment 1 | Treatment 2 | Treatment 3 |
|------------|-------------|-------------|-------------|
| Values | 63 | 83 | 70 |
| | 46 | 71 | 54 |
| | 53 | 87 | 61 |
| | 46 | 71 | 51 |
| Mean (\( \bar{x}_j \)) | 52 | 78 | 59 |
| Variance (\( s_j^2 \)) | 64.67 | 68.00 | 71.33 |
#### (a) Use analysis of variance to test for a significant difference among the means of the three treatments.
**State the null and alternative hypotheses.**
- **Correct Choice:**
- \( H_0: \mu_1 = \mu_2 = \mu_3 \)
- \( H_a: \) Not all the population means are equal.
**Find the value of the test statistic.**
- (Round your answer to two decimal places.)
- [Input box not filled, marked as incorrect]
**Find the p-value.**
- (Round your answer to three decimal places.)
- p-value = [Input box not filled, marked as incorrect]
**State your conclusion.**
- **Correct Option:**
- Reject \( H_0 \). There is sufficient evidence to conclude that the means of the three treatments are not equal.
This exercise involves using ANOVA to determine if there are any statistically significant differences between the means of the treatments.
![(b) **Use Fisher’s LSD procedure to determine which means are different.**
**Find the value of LSD.** (Round your answer to two decimal places.)
LSD = [Input Box] ❌
**Find the pairwise absolute difference between sample means for each pair of treatments.**
\[
| \bar{x}_1 - \bar{x}_2 | = 26 \quad ✔️
\]
\[
| \bar{x}_1 - \bar{x}_3 | = 7 \quad ✔️
\]
\[
| \bar{x}_2 - \bar{x}_3 | = 19 \quad ✔️
\]
**Which treatment means differ significantly? (Select all that apply.)**
- [x] There is a significant difference between the means for treatments 1 and 2.
- [ ] There is a significant difference between the means for treatments 1 and 3.
- [x] There is a significant difference between the means for treatments 2 and 3.
- [ ] There are no significant differences. ✔️](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6886f08-90b0-4bd9-a192-6e28f2935ee7%2Fa149accf-ccd5-4c6c-bf3e-96ab677cc711%2Fumcikki_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) **Use Fisher’s LSD procedure to determine which means are different.**
**Find the value of LSD.** (Round your answer to two decimal places.)
LSD = [Input Box] ❌
**Find the pairwise absolute difference between sample means for each pair of treatments.**
\[
| \bar{x}_1 - \bar{x}_2 | = 26 \quad ✔️
\]
\[
| \bar{x}_1 - \bar{x}_3 | = 7 \quad ✔️
\]
\[
| \bar{x}_2 - \bar{x}_3 | = 19 \quad ✔️
\]
**Which treatment means differ significantly? (Select all that apply.)**
- [x] There is a significant difference between the means for treatments 1 and 2.
- [ ] There is a significant difference between the means for treatments 1 and 3.
- [x] There is a significant difference between the means for treatments 2 and 3.
- [ ] There are no significant differences. ✔️
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