### Educational Website – Analysis of Poplar Tree Weights and Bonferroni Results#### Statistical Hypothesis Testing for Poplar Weights**Objective:**To determine if different treatments affect the mean weight of poplar trees.**Significance Level:**0.10**Hypotheses:**- **Null Hypothesis (H₀):** μ₁ = μ₂ = μ₃ = μ₄ (The mean weights are equal across all treatments).- **Alternative Hypothesis (H₁):** At least one mean is different.**Instructions:**1. **Test Statistic:** Calculate and round to two decimal places.2. **P-value:** Calculate and round to three decimal places.**Conclusion Options:**- **A:** Fail to reject H₀. Sufficient evidence to reject that treatments yield the same mean weight.- **B:** Fail to reject H₀. Insufficient evidence to reject that treatments yield the same mean weight.- **C:** Reject H₀. Insufficient evidence to reject that treatments yield the same mean weight.- **D:** Reject H₀. Sufficient evidence to reject that treatments yield the same mean weight.#### Interpretation of Bonferroni Results**Graphical Table Explanation:**- **Table Content:** - Treatment groups: No Treatment, Fertilizer, Irrigation, Fertilizer and Irrigation. - Recorded weights for each treatment.- **Bonferroni Results:** - Mean differences between treatments (I-J). - Standard Error. - Significance (Sig.) values, used to determine if differences are statistically significant.**Bonferroni Analysis Review:**- Evaluate if the mean differences are statistically significant by looking at the Sig. value.- A significance value below 0.10 indicates a significant difference between treatment means.**Next Step:**Examine how these results inform decision-making about the effectiveness of different treatments on the weight of poplar trees.

Solution: Given data isHypothesis HO: μ1 = μ2 =μ3 =μ4 H1: At least one of the four population means is different from the others. by using R software ANOVA Table is Test statistic is 7.21 P-value = 0.003 conclusion for this hypothesis test P-value=0.003 <0.1 so reject the Ho. Correct option is (d) Reject Ho There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight R-code value<-c(0.17,0.46,0.48,1.15,1.31,0.49,0.49,0.72,0.99,1.02,0.06,0.07,0.63,0.82,0.88,0.87,1.51,1.76,1.88,2.37)group1 <- c(rep("Group1", 5), rep("Group2", 5), rep("Group3", 5), rep("Group4", 5))my.dataframe<-data.frame(value, group1)res.aov <- aov(value ~ group1, data = my.dataframe)summary(res.aov) b)the displayed Bonferroni results tell us There is not a significant difference between the No Treatment and Fertilizer groups. There is not a significant difference between the No Treatment and Irrigation groups. There is a significant difference between the No Treatment and Fertilizer and Irrigation groups.