Question

To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.

Machine 1	Machine 2	Machine 3	Machine 4
6.5	9.1	10.7	9.7
8.1	7.6	10.1	12.4
5.6	9.8	9.3	11.9
7.6	10.3	9.9	10.5
8.5	9.4	8.8	11.1
7.5	10.2	8.8	11.0

(a) At the α = 0.05 level of significance, what is the difference, if any, in the population mean times among the four machines?

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃ = μ₄

H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ H_a: μ₁ = μ₂ = μ₃ = μ₄    

H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

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 = μ₄
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.

Reject H₀. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.

Do not reject H₀. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.    

Do not reject H₀. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.Reject H₀.

There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.

(b)Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a 0.05 level of significance.

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

LSD =

Find the pairwise absolute difference between sample means for machines 2 and 4

= x₂ − x₄

What conclusion can you draw after carrying out this test?

There is a significant difference between the means for machines 2 and 4.

There is not a significant difference between the means for machines 2 and 4.    

Answer 1

a)

H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: Not all the population means are equal.

value of the test statistic =16.06

p value =0.000

Reject H₀. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.

b)

Fisher's (LSD) for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =

1.15

x₂ − x₄ =1.7

There is a significant difference between the means for machines 2 and 4.