Question

Develop the analysis of variance computations for the following completely randomized design. At α = 0.05, is there a significant difference between the treatment means?

	Treatment
	A	B	C
	136	108	92
	119	115	81
	112	124	85
	107	103	102
	131	107	88
	113	108	118
	129	96	111
	113	115	120
		103	97
		81	106
xj	120	106	100
sj2	112.86	137.56	187.56

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

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

Answer 1

(a)

Correct option:

H0:

Ha:

(b)

From the given data, the following Table is constructed.

	Treatment A	Treatment B	Treatment C	Total
N	8	10	10	28
	960	1060	1000	3020
Mean	960/8=120	1060/10=106	1000/10=100	3020/28=107.857
	115990	113598	101688	331276
Std. Dev.	10.6234	11.7284	13.6951	14.3339

From the above Table, ANOVA Table is calculated as follows:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Sum of Squares	F
Between treatments	1831.4286	2	1831.4286/2=915.7143	915.7143/148.64=6.1606
Within treatments	3716	25	3716/25=148.64
Total	5547.4286	27

Test Statistic is given by:

F = 915.7143/148.64= 6.16

(c)

Degrees of freedom for numerator = 2

Degrees of freedom for denominator = 25

By Technology, P - Value = 0.0067

(d)

Correct option:

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