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
19	29	21
25	27	19
24	32	23
28	28	25

(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: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃

H₀: μ₁ ≠ μ₂ ≠ μ₃
H_a: μ₁ = μ₂ = μ₃   

H₀: μ₁ = μ₂ = μ₃
H_a: μ₁ ≠ μ₂ ≠ μ₃

H₀: 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: 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 three decimal places.)

p-value =

State your conclusion.

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.

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 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.

(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. or

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	104.00	2	52.00	6.16	0.0207
Within	76.00	9	8.44
Total	180.00	11

a)

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

value of the test statistic =6.16

p value =0.021

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)   =					4.65

x1-x3

2.00

not significant difference

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