### Transcription for Educational Website#### b. Analysis of Bonferroni ResultsThe Bonferroni results inform us that:- **There is a significant difference between the No Treatment and Fertilizer groups.**- **There is a significant difference between the No Treatment and Irrigation groups.**- **There is a significant difference between the No Treatment and Fertilizer and Irrigation groups.**#### c. Bonferroni Test ProcedureUsing the Bonferroni test with a 0.10 significance level, we determine if there's a significant difference between the mean amount of the irrigation treatment group and the group treated with both fertilizer and irrigation.##### Steps for Analysis:1. **Test Statistic:** - [Input the calculated value, rounded to two decimal places as needed.]2. **P-value:** - [Input the calculated value, rounded to three decimal places as needed.]##### Result Interpretation:- **Option A:** Reject \( H_0 \). There is insufficient evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight. - **Option B:** Fail to reject \( H_0 \). There is sufficient evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight. - **Option C:** Fail to reject \( H_0 \). There is insufficient evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight. - **Option D:** Reject \( H_0 \). There is sufficient evidence to warrant rejection of the claim that the irrigation treatment group and the group treated with both fertilizer and irrigation yield the same mean poplar weight.**Note:** Please fill in the test statistic and P-value where indicated for a complete analysis. # Educational Resource: Analyzing Poplar Weight Data with Bonferroni Tests## OverviewThis example explores the effect of different treatments on the mean weight of poplar trees. Poplar weights were measured in kilograms (kg) from trees subjected to different treatments in a rich and moist environment. The aim is to test the hypothesis that these treatments do not result in significantly different mean weights.### Hypothesis TestingWe use a significance level of 0.10 for this test.#### Null and Alternative Hypotheses- **Null Hypothesis (H₀):** The treatments result in the same mean poplar weight.- **Alternative Hypothesis (H₁):** The treatments result in different mean poplar weights.#### Tasks1. **Find the Test Statistic:** - Calculation involves determining the variance among the treatment groups. - Results should be rounded to two decimal places. 2. **Find the P-value:** - Calculation of the probability to observe the outcomes given that the null hypothesis is true. - Results should be rounded to three decimal places.### Bonferroni ResultsThe table details the mean differences between treatments alongside their statistical significance.#### Poplar Weights (kg)There are four categories:- **No Treatment:** Weights range from 0.17 kg to 1.31 kg.- **Fertilizer:** Weights range from 0.49 kg to 1.02 kg.- **Irrigation:** Weights range from 0.06 kg to 0.88 kg.- **Fertilizer and Irrigation:** Weights range from 0.87 kg to 1.76 kg.#### Statistical Comparisons- **Mean Difference (I-J):** Reflects the difference in mean weights between treatments I and J.- **Std. Error:** The standard error of the difference.- **Sig.:** Significance level determining if the difference is statistically meaningful.### ConclusionsBased on the significance:- **A.** Fail to reject H₀: There's enough evidence to reject the claim that all treatments yield the same result.- **B.** Fail to reject H₀: There's insufficient evidence to reject this claim.- **C.** Reject H₀: There's insufficient evidence to support the claim that treatments yield the same weight.- **D.** Reject H₀: There's sufficient evidence to support rejection of the

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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). H Click the icon to view the data table of the poplar weights and the Bonferroni results. - X Poplar weights (kg) and bonferroni results 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. No Treatment Fertilizer Irrigation Fertilizer and Irrig Họ 1.15 0.99 0.06 0.87 0.46 0.72 0.63 1.88 0.48 0.49 0.07 1.51 Find the test statistic. 0.17 0.49 0.82 2.37 (Round to two decimal places as needed.) 1.31 1.02 0.88 1.76 Find the P-value. Bonferroni Results Mean Difference (I-J) Std. Error - 0.0280 P.value = (Round to three decimal places as needed.) (1) TREATMENT 1.00 (J) TREATMENT 2.00 Sig. 1.000 0.24013 0.24013 What is the conclusion for this hypothesis test? 0.2220 – 0.9640 3.00 1.000 4.00 0.24013 0.019 O A. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight. O B. Fail to reject Ho There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight. OC. Reject Ho. There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight. O D. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight. Drint Dene

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P