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	27	21
27	26	20
24	31	23
24	28	16

(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: Not all the population means are equal.

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

9.93

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

p-value = 0.0053

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.

(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.

|x₁ ? x₃| = ____________

What conclusion can you draw after carrying out this test?

C} There is a signicant difference between the means for manufacturer 1 and manufacturer 3. C} There is not a signicant difference between the means for manufacturer 1 and manufacturer 3