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	27	20
26	25	18
24	32	24
26	32	26

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

= 0.05.

State the null and alternative hypotheses.

• H₀:₁=₂=₃ H_a:₁₂₃H₀:
• Not all the population means are equal. H_a:₁=₂=₃
• H₀:₁=₂=₃ H_a: Not all the population means are equal.
• H₀:₁₂₃ H_a:₁=₂=₃H₀:
• At least two of the population means are equal. H_a: At least two of the population means are different.

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

Find thep-value. (Round your answer to three decimal places.)p-value =

State your conclusion.

• RejectH₀. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer.
• Do not rejectH₀. 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.
• RejectH₀. 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 rejectH₀. 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= 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.

x₁x₃

=

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.