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 24

27 25 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: ?₁ ≠ ?₂ ≠ ?₃H₀: ?₁ ≠ ?₂ ≠ ?₃
H_a: ?₁ = ?₂ = ?₃ H₀: ?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: 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 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.

(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.

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	24
27	25	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: ?₁ ≠ ?₂ ≠ ?₃H₀: ?₁ ≠ ?₂ ≠ ?₃
H_a: ?₁ = ?₂ = ?₃ H₀: ?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: 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 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.

(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.

Accepted Answer

a) 
By applying the ANOVA test for a single factor,
The Null and alternative hypothesis:
Ho:  µ1 =…

Manufacturer 1 2 3 19 29 21 26 26 19 24 32 24 27 25 16 (a) Use these data to test whether the p