18. Bonferroni Test Shown below are weights (kg) of poplar trees obtained from t

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 1.21 0.57 0.56 0.13 1.30 Fertilizer 0.94 0.87 0.46 0.58 1.03 Irrigation 0.07 0.66 0.10 0.82 0.94 Fertilizer and Irrigation 0.85 1.78 1.47 2.25 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- ference between the mean amount of the irrigation treatment group and the group treated with 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 ( 95% Confidence Interval Std ErrorSig Lower Bound Upper Bound 7889 10469 0331 O TREATMENT (J) TREATMENT 1 00 2.00 3.00 4.00 02200 26955 23600 26955 26955 1.000 1.000 039 8329 5749 1 6549 84400

Explanation / Answer

Result:

b).

Bonferroni SPSS result shows the mean difference between all pairs of the groups, their standard error , p value associated with the difference. 95% confidence interval for the difference also displayed.

c).

From the partial result displayed, p value for difference between group1 and group 4 is 0.039 which is < 0.05 level of significance. The difference is significant.

The difference between group1 with group2 and 3 are not significant, P=1.0 which is > 0.05 level.

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