To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturer a chemical company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 28 26 24 30 22 20 20 27 18

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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 obtained the following data on the time (in minutes) needed to mix the material.
Manufacturer
1
3
28
| 26
20
27
18
30
22
25
24
24
(a) Use these data to test whether the population mean times for mixing a batch of material differ for the three
manufacturers. Use a = 0.05.
State the null and alternative hypotheses.
O Ho: Hy = Hz = Hz
%3D
: Not all the population means are equal.
Ha
Hoi Hy = Hz = Hz
O Hoi Hq # Hz # Hz
Ho: At least two of the population means are equal.
H: At least two of the population means are different.
O Ho: Not all the population means are equal.
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
2.
20
24
Transcribed Image Text: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 3 28 | 26 20 27 18 30 22 25 24 24 (a) Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a = 0.05. State the null and alternative hypotheses. O Ho: Hy = Hz = Hz %3D : Not all the population means are equal. Ha Hoi Hy = Hz = Hz O Hoi Hq # Hz # Hz Ho: At least two of the population means are equal. H: At least two of the population means are different. O Ho: Not all the population means are equal. 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 2. 20 24
State your conclusion.
O Reject H.. 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.
O Do not reject Ho. There is sufficient evidence to conclude that the mean time needed to mix a batch of material
is not the same for each manufacturer.
O Reject H.. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not
the same for each manufacturer.
O Do not reject H.. 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 a = 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.
=
What conclusion can you draw after carrying out this test?
O There is a significant difference between the means for manufacturer 1 and manufacturer 3.
O There is not a significant difference between the means for manufacturer 1 and manufacturer 3.
Transcribed Image Text:State your conclusion. O Reject H.. 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. O Do not reject Ho. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. O Reject H.. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. O Do not reject H.. 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 a = 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. = What conclusion can you draw after carrying out this test? O There is a significant difference between the means for manufacturer 1 and manufacturer 3. O There is not a significant difference between the means for manufacturer 1 and manufacturer 3.
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