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. No treatment Fertilizer Irrigation Fertilizer and Irrigation 1.26 1.02 0.09 0.81 0.47 .86 .52 1.71 0.45 0.55 0.06 1.45 0.14 0.67 0.79 2.37 1.33 0.97 0.76 1.66 (I) TREATMENT (J) TREATMENT Difference (I-J) Std. Error Sig. 1.00 2.00 −0.0840 0.28375 1.000 3.00 0.2860 0.28375 1.000 4.00 −0.8720 0.28375 0.037 1. Use a 0.10 significance level to test the claim that the different treatments result in the same mean weight. a. Determine the null and alternative hypotheses. 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? b. What do the displayed Bonferroni results tell us? 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?

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Description: 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 th

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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.

No treatment	Fertilizer	Irrigation	Fertilizer and Irrigation
1.26	1.02	0.09	0.81
0.47	.86	.52	1.71
0.45	0.55	0.06	1.45
0.14	0.67	0.79	2.37
1.33	0.97	0.76	1.66

(I) TREATMENT	(J) TREATMENT	Difference (I-J)	Std. Error	Sig.
1.00	2.00	−0.0840	0.28375	1.000
	3.00	0.2860	0.28375	1.000
	4.00	−0.8720	0.28375	0.037

1. Use a 0.10 significance level to test the claim that the different treatments result in the same mean weight.

a. Determine the null and alternative hypotheses.

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?

b. What do the displayed Bonferroni results tell us?

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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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