ou may need to use the appropriate technology to answer this question.The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment1 Treatment2 Treatment3 62 82 70 46 71 53 53 87 60 39 64 45 xj 50 76 57 sj 2 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. H 0: ?1 ≠ ?2 ≠ ?3 H a: ?1 = ?2 = ?3 H 0: ?1 = ?2 = ?3 H a: Not all the population means are equal.H 0: Not all the population means are equal. H a: ?1 = ?2 = ?3 H 0: ?1 = ?2 = ?3 H a: ?1 ≠ ?2 ≠ ?3 H 0: 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 thep-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not rejectH 0. There is sufficient evidence to conclude that the means of the three treatments are not equal.RejectH 0. There is sufficient evidence to conclude that the means of the three treatments are not equal. Do not rejectH 0. There is not sufficient evidence to conclude that the means of the three treatments are not equal.RejectH 0. 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.

ou may need to use the appropriate technology to answer this question. The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment 1 Treatment 2...

ou may need to use the appropriate technology to answer this question.

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_j ²	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.

H
₀: ?₁ ≠ ?₂ ≠ ?₃

H
_a: ?₁ = ?₂ = ?₃
H
₀: ?₁ = ?₂ = ?₃

H
_a: Not all the population means are equal.H
₀: Not all the population means are equal.

H
_a: ?₁ = ?₂ = ?₃
H
₀: ?₁ = ?₂ = ?₃

H
_a: ?₁ ≠ ?₂ ≠ ?₃
H
₀: 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 thep-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not rejectH
₀. There is sufficient evidence to conclude that the means of the three treatments are not equal.RejectH
₀. There is sufficient evidence to conclude that the means of the three treatments are not equal. Do not rejectH
₀. There is not sufficient evidence to conclude that the means of the three treatments are not equal.RejectH
₀. 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.

Jun 10, 2022

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