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# Poplar Tree Experiment Weights (kg) of poplar trees were

## Problem 2RE Chapter 12.3

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition

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Problem 2RE

Poplar Tree Experiment? Weights (kg) of poplar trees were obtained from trees planted in one region that was rich and moist and a second region that was sandy and dry. The trees were given different treatments as identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc.; the Minitab results are displayed. What do you conclude?

Step-by-Step Solution:

Solution 2RE Step 1: The given data are the weights of poplar tree planted in two different regions. The trees are given four different treatments. Then, the given data are categorized according to two factors. The two factors are regions where the trees are planted and four different treatments given to the trees. The Minitab two-way analysis of variance display with the given data is considered below: Step 2: in two-way analysis of variance,the procedure is starting by testing the interaction effect between regions and treatments given to the trees. The null hypothesis is given by Null hypothesis(H ):0The null hypothesis states that, there is no interaction between regions where the trees are planted and treatments given to the trees. Step 3: From the given Minitab display, it is seen that, there are two categories of regions where the trees are planted (rich, moist and sandy, dry). Similarly, there are four categories of treatments given to the trees (no treatment, fertilizer, irrigation and fertilizer, irrigation). Using the given Minitab display, the test statistic for testing the above null hypothesis can be defined as, mean square( interaction) F = mean square (error) = 0.05721 0.33521 = 0.1706 The value of the test statistic is 0.17. Step 4: in this case two-way analysis of variance is one tailed test. The p-value is 0.915 and the degrees of freedom 3 and 32. Comparing the p-value with the level of significance 0.05. Here the p-value is more than the level of significance 0.05. So the null hypothesis can not be rejected, we accept H . 0 Step 5: Here we conclude that there is a sufficient evidence to believe that,there is no interaction between regions where the trees are planted and treatments given to the trees. Step 6: Now to test the effect of regions where the trees are planted on the weights of the trees the following null hypothesis is used. Null hypothesis(H ): The null hypothesis states that, there is no effect of regions where 0 the trees are planted on the weights of the trees. Using the given Minitab display, the test statistic for testing the above null hypothesis can be defined as, mean square( Site) 0.27225 F = mean square (error)0.33521= 0.8121. The value of test statistic is 0.81

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