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
21	29	21
25	25	19
24	31	24
18	31	20

(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.

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.) State your conclusion.

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.

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 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.

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.

x₁x_{3 =}

=

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.