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 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
123
202821
252720
253022
263125


(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.



1. H
0: μ1 ≠ μ2 ≠ μ3


    H
a: μ1 = μ2 = μ3


2. H
0: Not all the population means are equal.

    H
a: μ1 = μ2 = μ3


3. H
0: At least two of the population means are equal.

    H
a: At least two of the population means are different.


4. H
0: μ1 = μ2 = μ3


    H
a: μ1 ≠ μ2 ≠ μ3


5. H
0: μ1 = μ2 = μ3


    H
a: Not all the population means are equal.



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 =


State your conclusion.


1. 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.

2. 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.

3. 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.

4. 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.

/x1 − x3/=








What conclusion can you draw after carrying out this test?


1. There is a significant difference between the means for manufacturer 1 and manufacturer 3.

2. There is not a significant difference between the means for manufacturer 1 and manufacturer 3.



Jun 01, 2022
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