Question

The following data are from a completely randomized design.

	Treatment
	A	B	C
	163	141	127
	142	156	122
	166	125	137
	145	142	141
	149	137	151
	165	145	120
Sample mean	155	141	133
Sample variance	118.0	102.8	146.0

(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: 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_C    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_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.

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

Answer 1

Solution:

We can use the excel ANOVA data analysis tool to find the answer to the given questions. The excel output is given below:

(a) Compute the sum of squares between treatments.

Answer:

(b) Compute the mean square between treatments.

Answer:

(c) Compute the sum of squares due to error.

Answer:

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

Answer:

(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.)

Answer:

(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.

Answer: H₀: 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.)

Answer:

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

Answer:

State your conclusion.

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