The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment1Treatment2Treatment3 638268 467355 548860 376145 xj507657 sj2123.33138.0092.67 (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: At least two of the population means are equal.Ha: At least two of the population means are different. H0: ?1 = ?2 = ?3Ha: ?1 ≠ ?2 ≠ ?3 H0: Not all the population means are equal.Ha: ?1 = ?2 = ?3 H0: ?1 = ?2 = ?3Ha: Not all the population means are equal. H0: ?1 ≠ ?2 ≠ ?3Ha: ?1 = ?2 = ?3Find 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 not 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.(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.

Applying ANOVA: value of the test statistic =7.44 p value =0.012 Fisher's (LSD) for group i and…

Answered: Which treatment means differ…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section: Chapter Questions

Problem 31P

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Question

The following data are from a completely randomized design. In the following calculations, use ? = 0.05.

	Treatment 1	Treatment 2	Treatment 3
	63	82	68
	46	73	55
	54	88	60
	37	61	45
x_j	50	76	57
s_j²	123.33	138.00	92.67

(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: At least two of the population means are equal.
H_a: At least two of the population means are different.

H₀: ?₁ = ?₂ = ?₃
H_a: ?₁ ≠ ?₂ ≠ ?₃

H₀: Not all the population means are equal.
H_a: ?₁ = ?₂ = ?₃

H₀: ?₁ = ?₂ = ?₃
H_a: Not all the population means are equal.

H₀: ?₁ ≠ ?₂ ≠ ?₃
H_a: ?₁ = ?₂ = ?₃

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 not 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.

(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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