Question

The following data are from a completely randomized design.

	Treatment
	A	B	C
	163	141	126
	143	157	123
	165	124	139
	144	142	141
	148	135	151
	173	153	124
Sample mean	156	142	134
Sample variance	159.2	144.0	129.6

(a)

Compute the sum of squares between treatments.

(b)

Compute the mean square between treatments.

(c)

Compute the sum of squares due to error.

(d)

Compute the mean square due to error. (Round your answer to two decimal places.)

(e)

Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments
Error
Total

(f)

At the α = 0.05 level of significance, test whether the means for the three treatments are equal.

State the null and alternative hypotheses.

H₀: μ_A ≠ μ_B ≠ μ_C
H_a: μ_A = μ_B = μ_CH₀: μ_A = μ_B = μ_C
H_a: μ_A ≠ μ_B ≠ μ_C    H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: Not all the population means are equal.
H_a: μ_A = μ_B = μ_CH₀: μ_A = μ_B = μ_C
H_a: Not all the population means are equal.

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

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

p-value =

State your conclusion.

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

Answer 1

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(a)

Compute the sum of squares between treatments. 1488

(b)

Compute the mean square between treatments. 744

(c)

Compute the sum of squares due to error. 2164

(d)

Compute the mean square due to error. 144.27 (Round your answer to two decimal places.)

(e)

Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Source	SS	df	MS	F	p-value
Treatment	1,488	2	744.00	5.16	.0197
Error	2,164	15	144.27
Total	3,652	17

f)

H_a: μ_A = μ_B = μ_CH₀: μ_A = μ_B = μ_C
H_a: Not all the population means are equal.

Find the value of the test statistic. (Round your answer to two decimal places.) 5.16

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

p-value =0.0197

State your conclusion.

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