Question

18. Bonferroni Test Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table be- low. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Also shown are partial results from using the Bonferroni test with the sample data. No Treatment Fertilizer and Irrigation Fertilizer Irrigation 1.21 0.94 0.07 0.85 0.57 0.87 0.66 1.78 0.56 0.10 0.46 1.47 0.13 0.58 0.82 2.25 1.03 1.30 0.94 1.64 a. Use a 0.05 significance level to test the claim that the different treatments result in the same mean weight. b. What do the displayed Bonferroni SPSS results tell us? c. Use the Bonferroni test procedure with a 0.05 significance level to test for a significant dif- both fertilizer and irrigation. Identify the test statistic and either the P-value or critical values. What do the results indicate? Bonferroni Results from SPSS Mean Difference ( J) 95% Confidence Interval Std.ErrorSig. Lower Bound Upper Bound O TREATMENT TREATMENT 1.00 2.00 02200 26955 1.000 7889 -8329 3.00 23600 269551.000 1.0469 5749 4.00 84400 -,0331 26955 039 -1.6549

Answer 1

Answer:

a) To test the hypothesis is that the different treatments result in the different mean weight at 5% level of significance. The null and alternative hypothesis is, Ha:at least one u, is unequal.

The F-test statistics is, By using MINITAB software, find F-test statistics with the help of following steps: 1) Import the data 2) Choose One-Way from ANOVA in Stat menu. 3) Choose Response variable and Factor Variable 4) Click Ok. One-way ANOVA: Frequency versus Group Source DF SS MS F Group 3 3.346 1.115 6.14 0.006 Error 16 2.906 0.182 Total 19 6.253

The conclusion is that p-value in this context is less than 0.05 which is 0.0001, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the different treatments result in the different mean weight. The result is statistically significant.

b) The displayed Bonferroni results tell us which treatment of mean weight is actually different.

c) From the SPSS output, the Bonferroni test concludes the p-value is less than 0.05, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the mean difference of amount of irrigation Treatment 1-Treatment 4 is significant. The result is statistically significant.