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 20 25 25 19 24 31 22 23 28 23 (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 1 2 3 H a 1 2 3 H 0 1 2 3 H a Not all the population means are equal 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 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 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 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 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

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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	20
25	25	19
24	31	22
23	28	23

(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: ₁ ₂ ₃H₀: ₁ = ₂ = ₃ H_a: Not all the population means are equal. 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: ₁ = ₂ = ₃H₀: 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 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.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 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 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?

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.