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 28 19 26 26 20 25 30 23 25 24 22 (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 H 0 At least two of the population means are equal H a At least two of the population means are different H 0 1 2 3 H a 1 2 3 H 0 1 2 3 H a 1 2 3 H 0 1 2 3 H a Not all the population means are equal H 0 Not all the population means are equal H a 1 2 3 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 Do not reject H 0 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 H 0 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 H 0 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 H 0 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 x 1 x 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

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on May 19, 2024

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

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	28	19
26	26	20
25	30	23
25	24	22

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