A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination.
A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants.
| Plant 1 Atlanta |
Plant 2 Dallas |
Plant 3 Seattle | ||
|---|---|---|---|---|
| 85 | 71 | 59 | ||
| 75 | 75 | 64 | ||
| 82 | 73 | 62 | ||
| 76 | 74 | 69 | ||
| 71 | 69 | 75 | ||
| 85 | 82 | 67 | ||
| Sample mean |
79 | 74 | 66 | |
| Sample variance |
34.0 | 20.0 | 32.0 | |
| Sample standard deviation |
5.83 | 4.47 | 5.66 |
Set up the ANOVA table for these data. (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 |
Mean Square |
F | p-value |
|---|---|---|---|---|---|
| Treatments | 516 | 2 | 258 | ? | ? |
| Error | ? | 15 | ? | ||
| Total | ? | 17 |
Test for any significant difference in the mean examination score for the three plants. Use
? = 0.05.
State the null and alternative hypotheses.
-H0: ?1 = ?2 = ?3
Ha: ?1 ≠ ?2 ≠ ?3
Ha: ?1 ≠ ?2 ≠ ?3
-H0: ?1 = ?2 = ?3
Ha: Not all the population means are equal.
Ha: Not all the population means are equal.
- H0: ?1 ≠ ?2 ≠ ?3
Ha: ?1 = ?2 = ?3
Ha: ?1 = ?2 = ?3
-H0: At least two of the population means are equal.
Ha: At least two of the population means are different.
Ha: At least two of the population means are different.
-H0: Not all the population means are equal.
Ha: ?1 = ?2 = ?3
Ha: ?1 = ?2 = ?3
Find the value of the test statistic. (Round your answer to two decimal places.)
Test statistic=??
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 means for the three plants are not equal.
-Reject H0. There is sufficient evidence to conclude that the means for the three plants are not equal.
-Reject H0. There is not sufficient evidence to conclude that the means for the three plants are not equal.
-Do not reject H0. There is sufficient evidence to conclude that the means for the three plants are not equal.
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A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table.
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