A task requires the completion of four activities. A teacher would like to know if differences in the sequence of the four activities results in different task completion times. The teacher selects three students and demonstrates the activities in random order to the students. Then each student completes the task with each of the activity sequences. The completion times are recorded. The following table shows the minutes for each student to complete each task. Students (minutes) Sequence Allen Carla Henry A 22.4 20.8 21.5 B 17.0 19.4 20.7 C 19.2 20.2 21.2 D 20.3 18.6 20.4 Click here for the Excel Data File Required: a-1. Identify the right option for Treatments (Students). Null hypothesis: H0: μA = μC = μH H0: μA ≠ μC ≠ μH multiple choice 1 a b Alternate hypothesis: multiple choice 2 All means are the same. Not all means are the same. a-2. Identify the right option for Blocks (Sequence). Null hypothesis: H0: μA ≠ μB ≠ μC ≠ μD H0: μA = μB = μC = μD multiple choice 3 a b Alternate hypothesis: multiple choice 4 Not all means are the same. All means are the same. b. What are the test statistics? (Round your answers to 4 decimal places.) c. What are the p-values? (Round your answers to 4 decimal places.) d. Using a 0.05 significance level, what is your decision regarding the null hypotheses? e-1. Interpret the result for treatments. e-2. Interpret the result for blocks.
A task requires the completion of four activities. A teacher would like to know if differences in the sequence of the four activities results in different task completion times. The teacher selects three students and demonstrates the activities in random order to the students. Then each student completes the task with each of the activity sequences. The completion times are recorded. The following table shows the minutes for each student to complete each task.
| Students (minutes) | |||
| Sequence | Allen | Carla | Henry |
| A | 22.4 | 20.8 | 21.5 |
| B | 17.0 | 19.4 | 20.7 |
| C | 19.2 | 20.2 | 21.2 |
| D | 20.3 | 18.6 | 20.4 |
Click here for the Excel Data File
Required:
a-1. Identify the right option for Treatments (Students).
Null hypothesis:
-
H0: μA = μC = μH
-
H0: μA ≠ μC ≠ μH
multiple choice 1
-
a
-
b
Alternate hypothesis:
multiple choice 2
-
All means are the same.
-
Not all means are the same.
a-2. Identify the right option for Blocks (Sequence).
Null hypothesis:
-
H0: μA ≠ μB ≠ μC ≠ μD
-
H0: μA = μB = μC = μD
multiple choice 3
-
a
-
b
Alternate hypothesis:
multiple choice 4
-
Not all means are the same.
-
All means are the same.
b. What are the test statistics? (Round your answers to 4 decimal places.)
c. What are the p-values? (Round your answers to 4 decimal places.)
d. Using a 0.05 significance level, what is your decision regarding the null hypotheses?
e-1. Interpret the result for treatments.
e-2. Interpret the result for blocks.
Given data:
| Sequence | Allen | Carla | Henry |
| A | 22.4 | 20.8 | 21.5 |
| B | 17 | 19.4 | 20.7 |
| C | 19.2 | 20.2 | 21.2 |
| D | 20.3 | 18.6 | 20.4 |
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