In: Statistics and Probability
You may need to use the appropriate technology to answer this question.
To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.
You may need to use the appropriate technology to answer this question. To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.
(a) At the α = 0.05 level of significance, what is the difference, if any, in the population mean times among the four machines? State the null and alternative hypotheses. 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. (b) Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a 0.05 level of significance. Find the value of LSD. (Round your answer to two decimal places.) LSD = Find the pairwise absolute difference between sample means for machines 2 and 4. {x2 − x4} = |
|||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(a)
At the α = 0.05 level of significance, what is the difference, if any, in the population mean times among the four machines?
State the null and alternative hypotheses.
H0: μ1 ≠
μ2 ≠ μ3 ≠
μ4
Ha: μ1 =
μ2 = μ3 =
μ4H0: Not all the
population means are equal.
Ha: μ1 =
μ2 = μ3 =
μ4 H0:
μ1 = μ2 =
μ3 = μ4
Ha: Not all the population means are
equal.H0: μ1 =
μ2 = μ3 =
μ4
Ha: μ1 ≠
μ2 ≠ μ3 ≠
μ4H0: At least two of the
population means are equal.
Ha: At least two of the population means are
different.
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.
Reject H0. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.Do not reject H0. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. Reject H0. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.Do not reject H0. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines.
(b)
Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a 0.05 level of significance.
Find the value of LSD. (Round your answer to two decimal places.)
LSD =
Find the pairwise absolute difference between sample means for machines 2 and 4.
x2 − x4
=
What conclusion can you draw after carrying out this test?