The accompanying data are the weights (kg) of poplar trees that were obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the accompanying table. Also shown are partial results from using the Bonferroni test with the sample data. Complete parts (a) through (c).
The accompanying data are the weights (kg) of poplar trees that were obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the accompanying table. Also shown are partial results from using the Bonferroni test with the sample data. Complete parts (a) through (c).
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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![The accompanying data are the weights (kg) of poplar trees that were obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the accompanying table. Also shown are partial results from using the Bonferroni test with the sample data. Complete parts (a) through (c).
---
**a. Use a 0.10 significance level to test the claim that the different treatments result in the same mean weight.**
- **Determine the null and alternative hypotheses:**
- \( H_0 \): [Enter hypothesis]
- \( H_1 \): [Enter hypothesis]
- **Determine the test statistic.**
- The test statistic is [Fill in the blank].
(Round to two decimal places as needed.)
- **Determine the P-value.**
- The P-value is [Fill in the blank].
(Round to three decimal places as needed.)
- **What is the conclusion for this hypothesis test at a 0.10 significance level?**
- A. Fail to reject \( H_0 \). There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
- B. Reject \( H_0 \). There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
- C. Fail to reject \( H_0 \). There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
- D. Reject \( H_0 \). There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
---
**b. What do the displayed Bonferroni results tell us?**
- With a P-value of [Enter P-value], there [significant/no significant] difference between the No Treatment and Fertilizer groups.
- With a P-value of [Enter P-value], there [significant/no significant] difference between the No Treatment and Irrigation groups.
- With a P-value of [Enter P-value], there [significant/no significant] difference between the No Treatment and Fertilizer and Irrigation groups.
(Round to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64d6ab45-be0f-4c5d-888e-4cab0739cade%2Fbd892826-e843-4edf-aac5-076eb8ac1cb6%2Fotdken_processed.png&w=3840&q=75)
Transcribed Image Text:The accompanying data are the weights (kg) of poplar trees that were obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the accompanying table. Also shown are partial results from using the Bonferroni test with the sample data. Complete parts (a) through (c).
---
**a. Use a 0.10 significance level to test the claim that the different treatments result in the same mean weight.**
- **Determine the null and alternative hypotheses:**
- \( H_0 \): [Enter hypothesis]
- \( H_1 \): [Enter hypothesis]
- **Determine the test statistic.**
- The test statistic is [Fill in the blank].
(Round to two decimal places as needed.)
- **Determine the P-value.**
- The P-value is [Fill in the blank].
(Round to three decimal places as needed.)
- **What is the conclusion for this hypothesis test at a 0.10 significance level?**
- A. Fail to reject \( H_0 \). There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
- B. Reject \( H_0 \). There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
- C. Fail to reject \( H_0 \). There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
- D. Reject \( H_0 \). There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
---
**b. What do the displayed Bonferroni results tell us?**
- With a P-value of [Enter P-value], there [significant/no significant] difference between the No Treatment and Fertilizer groups.
- With a P-value of [Enter P-value], there [significant/no significant] difference between the No Treatment and Irrigation groups.
- With a P-value of [Enter P-value], there [significant/no significant] difference between the No Treatment and Fertilizer and Irrigation groups.
(Round to three decimal places as needed.)
Transcribed Image Text:**Poplar Weights (kg) and Bonferroni Results**
This table provides the weights of poplars (in kilograms) under different treatment conditions: No Treatment, Fertilizer, Irrigation, and Fertilizer and Irrigation.
**Weights:**
- **No Treatment:**
- 1.211
- 0.567
- 0.559
- 0.129
- 1.297
- **Fertilizer:**
- 0.936
- 0.874
- 0.462
- 0.578
- 1.028
- **Irrigation:**
- 0.073
- 0.664
- 0.095
- 0.821
- 0.939
- **Fertilizer and Irrigation:**
- 0.849
- 1.777
- 1.471
- 2.252
- 1.642
**Bonferroni Results:**
The section below displays the Bonferroni pairwise comparison results:
- **(I) Treatment 1 vs (J) Treatment 2:**
- Mean Difference (I-J): -0.0230
- Standard Error: 0.26972
- Significance (Sig.): 1.000
- **(I) Treatment 1 vs (J) Treatment 3:**
- Mean Difference (I-J): 0.2342
- Standard Error: 0.26972
- Significance (Sig.): 1.000
- **(I) Treatment 1 vs (J) Treatment 4:**
- Mean Difference (I-J): -0.8456
- Standard Error: 0.26972
- Significance (Sig.): 0.038
**Buttons:**
- **Print:** Allows the user to print the results.
- **Done:** Indicates the completion of viewing or interaction with the results.
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