at a 0.10 significance level?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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).
Click the icon to view the data table of the poplar weights and the Bonferroni results.
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.
H₂!
H₁:
Determine the test statistic.
The test statistic is
(Round to two decimal places as needed.)
Determine the P-value.
The P-value is
(Round to three decimal places as needed.).
What is the conclusion for this hypothesis test at a 0.10 significance level?
▼
O A. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean po
OB. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weig
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. 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.
b. What do the displayed Bonferroni results tell us?
With a P-value of
With a P-value of
there
there
With a P-value of
there
(Round to three decimal places as needed.).
a significant difference between the No Treatment and Fertilizer groups.
a significant difference between the No Treatment and Irrigation groups.
H₂:
H₂:
a significant difference between the No Treatment and Fertilizer and Irrigation groups.
The test statistic is
(Round to two decimal places as needed.)
Find the P-value.
G
The P-value is
(Round to three decimal places as needed.)
What do the results indicate at a 0.10 significance level?
No Treatment
1.212
0.573
0.557
0.133
1.297
(1) TREATMENT
1.00
Fertilizer
0.939
0.866
0.464
0.577
1.029
Bonferroni Results
(J) TREATMENT
2.00
3.00
4.00
Print
Irrigation
0.069
0.661
0.098
0.817
0.935
OA. Reject H. 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.
OB. Fail to reject Ho. 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.
OC. Fail to reject Ho. 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.
D. Reject H. 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.
Mean
Difference (I-J) Std. Error
-0.0206
0.2384
-0.8422
Fertilizer and Irrigatio
0.852
1.776
Done
c. Let P₁, P₂, P3, and H, represent the mean amount of the no treatment, fertilizer, irrigation, and fertilizer and irrigation groups, respectively. Use the Bonferroni test procedure with a 0.10 significance level to test for a significant difference between the mean amount
of the irrigation treatment group and the group treated with both fertilizer and irrigation. Identify the test statistic and the P-value. What do the results indicate?
Determine the null and alternative hypotheses.
0.26898
0.26898
0.26898
1.466
2.252
1.637
Sig.
1.000
1.000
0.039
Transcribed Image Text: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). Click the icon to view the data table of the poplar weights and the Bonferroni results. 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. H₂! H₁: Determine the test statistic. The test statistic is (Round to two decimal places as needed.) Determine the P-value. The P-value is (Round to three decimal places as needed.). What is the conclusion for this hypothesis test at a 0.10 significance level? ▼ O A. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean po OB. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weig 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. 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. b. What do the displayed Bonferroni results tell us? With a P-value of With a P-value of there there With a P-value of there (Round to three decimal places as needed.). a significant difference between the No Treatment and Fertilizer groups. a significant difference between the No Treatment and Irrigation groups. H₂: H₂: a significant difference between the No Treatment and Fertilizer and Irrigation groups. The test statistic is (Round to two decimal places as needed.) Find the P-value. G The P-value is (Round to three decimal places as needed.) What do the results indicate at a 0.10 significance level? No Treatment 1.212 0.573 0.557 0.133 1.297 (1) TREATMENT 1.00 Fertilizer 0.939 0.866 0.464 0.577 1.029 Bonferroni Results (J) TREATMENT 2.00 3.00 4.00 Print Irrigation 0.069 0.661 0.098 0.817 0.935 OA. Reject H. 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. OB. Fail to reject Ho. 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. OC. Fail to reject Ho. 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. D. Reject H. 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. Mean Difference (I-J) Std. Error -0.0206 0.2384 -0.8422 Fertilizer and Irrigatio 0.852 1.776 Done c. Let P₁, P₂, P3, and H, represent the mean amount of the no treatment, fertilizer, irrigation, and fertilizer and irrigation groups, respectively. Use the Bonferroni test procedure with a 0.10 significance level to test for a significant difference between the mean amount of the irrigation treatment group and the group treated with both fertilizer and irrigation. Identify the test statistic and the P-value. What do the results indicate? Determine the null and alternative hypotheses. 0.26898 0.26898 0.26898 1.466 2.252 1.637 Sig. 1.000 1.000 0.039
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