MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.
Temperature | ||
---|---|---|
50°C | 60°C | 70°C |
34 | 31 | 24 |
23 | 32 | 28 |
37 | 34 | 27 |
38 | 23 | 30 |
28 | 25 | 36 |
Construct an analysis of variance table. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)
Source of Variation |
Sum of Squares |
Degrees of Freedom |
Square |
F | p-value |
---|---|---|---|---|---|
Treatments | |||||
Error | |||||
Total |
Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
State the null and alternative hypotheses.
H0: ?50°C = ?60°C = ?70°C
Ha: Not all the population means are equal.H0: Not all the population means are equal.
Ha: ?50°C = ?60°C = ?70°C H0: ?50°C ≠ ?60°C ≠ ?70°C
Ha: ?50°C = ?60°C = ?70°CH0: At least two of the population means are equal.
Ha: At least two of the population means are different.H0: ?50°C = ?60°C = ?70°C
Ha: ?50°C ≠ ?60°C ≠ ?70°C
Ha: Not all the population means are equal.H0: Not all the population means are equal.
Ha: ?50°C = ?60°C = ?70°C H0: ?50°C ≠ ?60°C ≠ ?70°C
Ha: ?50°C = ?60°C = ?70°CH0: At least two of the population means are equal.
Ha: At least two of the population means are different.H0: ?50°C = ?60°C = ?70°C
Ha: ?50°C ≠ ?60°C ≠ ?70°C
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal.Do not reject H0. There is sufficient evidence to conclude that the mean yields for the three temperatures are not equal. Reject H0. There is sufficient evidence to conclude that the mean yields for the three temperatures are not equal.Reject H0. There is not sufficient evidence to conclude that the mean yields for the three temperatures are not equal.
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