The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment 1 Treatment 2 Treatment 3 62 82 70 46 71 53 53 87 60 39 64 45 xj 50 76 57 sj2 96.67 108.67 112.67 (a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses. H0: ?1 ≠ ?2 ≠ ?3 Ha: ?1 = ?2 = ?3H0: ?1 = ?2 = ?3 Ha: Not all the population means are equal. H0: Not all the population means are equal. Ha: ?1 = ?2 = ?3H0: ?1 = ?2 = ?3 Ha: ?1 ≠ ?2 ≠ ?3H0: At least two of the population means are equal. Ha: At least two of the population means are different. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal.Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal. Do not reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.Reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal. (b) Use Fisher's LSD procedure to determine which means are different. Find the value of LSD. (Round your answer to two decimal places.) LSD = Find the pairwise absolute difference between sample means for each pair of treatments. x1 − x2 = x1 − x3 = x2 − x3 = Which treatment means differ significantly? (Select all that apply.) There is a significant difference between the means for treatments 1 and 2.There is a significant difference between the means for treatments 1 and 3.There is a significant difference between the means for treatments 2 and 3.There are no significant differences.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The following data are from a completely randomized design. In the following calculations, use

? = 0.05.

	Treatment 1	Treatment 2	Treatment 3
	62	82	70
46	71	53
53	87	60
39	64	45
x_j	50	76	57
s_j²	96.67	108.67	112.67

(a)

Use analysis of variance to test for a significant difference among the means of the three treatments.

State the null and alternative hypotheses.

H₀: ?₁ ≠ ?₂ ≠ ?₃
H_a: ?₁ = ?₂ = ?₃H₀: ?₁ = ?₂ = ?₃
H_a: Not all the population means are equal. H₀: Not all the population means are equal.
H_a: ?₁ = ?₂ = ?₃H₀: ?₁ = ?₂ = ?₃
H_a: ?₁ ≠ ?₂ ≠ ?₃H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that the means of the three treatments are not equal.Reject H₀. There is sufficient evidence to conclude that the means of the three treatments are not equal. Do not reject H₀. There is not sufficient evidence to conclude that the means of the three treatments are not equal.Reject H₀. There is not sufficient evidence to conclude that the means of the three treatments are not equal.

(b)

Use Fisher's LSD procedure to determine which means are different.

Find the value of LSD. (Round your answer to two decimal places.)

LSD =

Find the pairwise absolute difference between sample means for each pair of treatments.

x₁ − x₂

x₁ − x₃

x₂ − x₃

Which treatment means differ significantly? (Select all that apply.)

There is a significant difference between the means for treatments 1 and 2.There is a significant difference between the means for treatments 1 and 3.There is a significant difference between the means for treatments 2 and 3.There are no significant differences.

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