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
29
20
26
25
18
23
32
23
27
30
27
1. Use these data to test whether the population mean times for
mixing a batch of material differ for the three manufacturers.
Use
α = 0.05.
State the null and alternative hypotheses.
A.
H0: μ1 = μ2 = μ3
Ha: μ1 ≠ μ2 ≠ μ3H0:
B. At least two of the population means are equal.
Ha: At least two of the
population means are different.
C.
H0: μ1 = μ2 = μ3
Ha: Not all the population
means are equal
D.
H0: μ1 ≠ μ2 ≠ μ3
Ha: μ1 = μ2 = μ3H0:
E. Not all the population means are equal.
Ha: μ1 = μ2 = μ3
2. Find the value of the test statistic. (Round your answer to
two decimal places.)
3. Find the p-value. (Round your answer to three
decimal places.)
p-value =
4. State your conclusion.
A. 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. 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.
C. 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.
D. 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.
5. At the α = 0.05 level of significance, use Fisher's
LSD procedure to test for the equality of the means for
manufacturers 1 and 3.
A. Find the value of LSD. (Round your answer to two decimal
places.)
LSD =
B. Find the pairwise absolute difference between sample means
for manufacturers 1 and 3.
What conclusion can you draw after carrying out this test?
x1 − x3
C. A. There is a significant difference between the means for
manufacturer 1 and manufacturer 3.
B. There is not a significant difference
between the means for manufacturer 1 and manufacturer
3.