Question

To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, a chemical company obtained the following data on the time (in minutes) needed to mix the material.

Manufacturer
1	2	3
20	28	19
26	25	20
25	32	22
21	27	23

(a)

Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use

α = 0.05.

State the null and alternative hypotheses.

H₀: μ₁ ≠ μ₂ ≠ μ₃
H_a: μ₁ = μ₂ = μ₃H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.     H₀: μ₁ = μ₂ = μ₃
H_a: μ₁ ≠ μ₂ ≠ μ₃H₀: μ₁ = μ₂ = μ₃
H_a: Not all the population means are equal.H₀: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃

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 not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.Reject H₀. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.     Reject H₀. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.Do not reject H₀. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.

(b)

At the α = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3.

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

LSD =

Find the pairwise absolute difference between sample means for manufacturers 1 and 3.

x₁ − x₃

=

What conclusion can you draw after carrying out this test?

There is a significant difference between the means for manufacturer 1 and manufacturer 3.There is not a significant difference between the means for manufacturer 1 and manufacturer 3.     

Answer 1

Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array):

Source	SS	df	MS	F	P value
Between	104.0000	2	52.0000	7.5484	0.012
Within	62.0000	9	6.8889
Total	166.0000	11

a)

H0: μ1 = μ2 = μ3
Ha: Not all the population means are equal.

value of the test statistic =7.55

p-value =0.012

Reject H0. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.

b)

critical value of t with 0.05 level and N-k=9 degree of freedom=	tN-k=	2.262
Fisher's (LSD) for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =		4.20

x3-x1

2.00

not significant difference

.There is not a significant difference between the means for manufacturer 1 and manufacturer 3.