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
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 |
21 | 27 | 21 |
27 | 26 | 20 |
24 | 31 | 23 |
24 | 28 | 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 Ha: Not all the population means are equal.
Find the value of the test statistic. (Round your answer to two decimal places.)
9.93
Find the p-value. (Round your answer to three decimal places.)
p-value = 0.0053
State your conclusion:
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.
(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?
C} There is a signicant difference between the means for manufacturer 1 and manufacturer 3. C} There is not a signicant difference between the means for manufacturer 1 and manufacturer 3Step by Step Solution
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