The accompanying data are the weights (kg) of poplar trees that were obtained fr

Question

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).
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.
H0: a. Not all of the population means are equal.
b. 1=2=3=4
c. 1>2>3>4
d. Exactly two of the population means are equal.
e. 1234
f. At least two of the population means are equal.
H1: a.Exactly two of the population means are different from the others.
b. 1=2=3=4
c. 1>2>3>4
d. At least one of the four population means is different from the others.
e.At least two of the population means are equal.
f. 1234
Find the test statistic.
______
(Round to two decimal places as needed.)
Find the P-value.
P-value = _____
(Round to three decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Reject H0. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
B. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
C. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
D. Reject H0.There is insufficient 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?
There (is or is not) a significant difference between the No Treatment and Fertilizer groups.
There (is or is not) a significant difference between the No Treatment and Irrigation groups.
There (is or is not) a significant difference between the No Treatment and Fertilizer and Irrigation groups.
c. 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?
The test statistic is
____
(Round to two decimal places as needed.)
Find the P-value.
P-value ____
(Round to three decimal places as needed.)
What do the results indicate?
A. Reject H0. 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.
B. Fail to reject H0. 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.
C. Fail to reject H0. 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.
D. Reject H0. 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. 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).
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.
H0: a. Not all of the population means are equal.
b. 1=2=3=4
c. 1>2>3>4
d. Exactly two of the population means are equal.
e. 1234
f. At least two of the population means are equal.
H1: a.Exactly two of the population means are different from the others.
b. 1=2=3=4
c. 1>2>3>4
d. At least one of the four population means is different from the others.
e.At least two of the population means are equal.
f. 1234
Find the test statistic.
______
(Round to two decimal places as needed.)
Find the P-value.
P-value = _____
(Round to three decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Reject H0. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
B. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
C. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
D. Reject H0.There is insufficient 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?
There (is or is not) a significant difference between the No Treatment and Fertilizer groups.
There (is or is not) a significant difference between the No Treatment and Irrigation groups.
There (is or is not) a significant difference between the No Treatment and Fertilizer and Irrigation groups.
c. 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?
The test statistic is
____
(Round to two decimal places as needed.)
Find the P-value.
P-value ____
(Round to three decimal places as needed.)
What do the results indicate?
A. Reject H0. 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.
B. Fail to reject H0. 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.
C. Fail to reject H0. 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.
D. Reject H0. 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. Poplar Weights (kg) and Bonferroni Results No Treatment 1.27 0.47 0.45 0.16 1.26 Fertilizer 1.06 0.82 0.31 0.45 0.95 IrrigationFertilizer and Irrigation 0.09 0.52 0.09 0.63 0.89 0.87 1.78 1.52 2.28 1.83 Bonferroni Results Mean (D TREATMENT (J) TREATMENT Difference (I-J) Std. Error Sig. 1.000 0.26077 1000 0.26077 0.022 0.260771 2.00 3.00 4.00 1.00 00040 0.2780 0.9340

Explanation / Answer

We use Minitab for ANOVA,

Factor Information

Factor Levels Values
Factor 3 No Treatment, Fertilizer, Irrigation

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 0.2540 0.1270 0.78 0.480
Error 12 1.9525 0.1627
Total 14 2.2064

the null and alternative hypotheses are,

Ho : 1=2=3=4

H1 :  At least one of the four population means is different from the others.

the test statistic is   F = 0.78

the P-value is 0.480

P-value > 0.10 we reject null hypothesis

Results indicates that,

Reject H0. 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.

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