You may need to use the appropriatetechnologyto answer this 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
26	26	19
24	32	23
23	29	17

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

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 =

(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.