DOE Team member:
- Rong Yiren
- Tanapattanalux Kittitat
- Xavier Chua
- Benjamin Ang
FULL factorial data table
| Run# | Run Order | A | B | C | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | Ave. | Std.Dev. |
| 1 | 1 | - | - | - | 207.0 | 208.3 | 209.2 | 204.0 | 205.7 | 209.4 | 209.2 | 208.3 | 207.6 | 1.94 |
| 2 | 3 | + | - | - | 147.0 | 158.0 | 155.5 | 160.0 | 156.4 | 158.1 | 156.3 | 155.1 | 155.8 | 3.90 |
| 3 | 2 | - | + | - | 161.5 | 163.5 | 156.4 | 160.3 | 160.4 | 160.3 | 164.0 | 159.2 | 160.7 | 2.41 |
| 4 | 6 | + | + | - | 111.5 | 124.0 | 123.7 | 123.0 | 125.0 | 116.5 | 121.0 | 124.0 | 121.1 | 4.72 |
| 5 | 4 | - | - | + | 113.5 | 115.3 | 106.0 | 113.7 | 100.5 | 112.3 | 110.5 | 113.2 | 110.6 | 4.97 |
| 6 | 5 | + | - | + | 105.5 | 109.5 | 104.5 | 103.0 | 106.5 | 107.0 | 107.5 | 105.0 | 106.1 | 2.01 |
| 7 | 8 | - | + | + | 112.5 | 114.0 | 103.0 | 108.0 | 103.0 | 105.0 | 114.0 | 113.0 | 109.1 | 4.89 |
| 8 | 7 | + | + | + | 99.5 | 102.5 | 103.0 | 105.0 | 105.5 | 97.0 | 105.5 | 99.0 | 102.1 | 3.27 |
Fractional factorial data table
| Run# | Run Order | A | B | C | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | Ave. | Std.Dev. |
| 2 | 3 | + | - | - | 141.5 | 146.5 | 137.0 | 146.0 | 142.0 | 142.0 | 141.0 | 149.5 | 143.2 | 3.92 |
| 3 | 2 | - | + | - | 153.5 | 154.0 | 164.0 | 155.0 | 161.0 | 160.0 | 158.0 | 159.5 | 158.1 | 3.71 |
| 5 | 4 | - | - | + | 105.0 | 107.0 | 107.0 | 108.5 | 104.5 | 109.0 | 110.5 | 105.0 | 107.1 | 2.16 |
| 8 | 7 | + | + | + | 108.5 | 107.5 | 104.5 | 105.5 | 106.5 | 106.5 | 107.5 | 105.5 | 106.5 | 1.31 |
Scope of the test
Xavier Chua will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.
Benjamin Ang will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.
Tanapattanalux Kittitat will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.
I (Yiren) will use Run #8 from FRACTIONAL factorial and
Run#8 from FULL factorial.
Steps of hypothesis testing
|
The QUESTION |
The catapult (the ones that were used in the DOE practical)
manufacturer needs to determine the consistency of the products they have manufactured.
Therefore they want to determine whether CATAPULT A produces the same flying
distance of projectile as that of CATAPULT B. |
|
Scope of the
test |
The human factor is
assumed to be negligible. Therefore different user will not have any effect
on the flying distance of projectile.
Flying distance for
catapult A and catapult B is collected using the factors below: Arm length = 36 cm Start angle = 30 degree Stop angle = 90 degree |
|
Step 1: State the
statistical Hypotheses: |
State the null hypothesis
(H0): CATAPULT A produces the same flying distance of projectile as that of CATAPULT B. µ0 = µ1
State the alternative hypothesis (H1): CATAPULT A produces the different flying distance of projectile as that of CATAPULT B. µ0 ≠ µ1 |
|
Step 2: Formulate an
analysis plan. |
Sample size is 2 Therefore t-test will be used.
Since the sign of H1 is "≠", a two tailed test is used.
Significance level (α) used in this test is: 0.05
|
|
Step 3: Calculate the
test statistic |
State the mean and
standard deviation of sample catapult A: Mean = 102.1 m Standard deviation = 3.27 State the mean and
standard deviation of sample catapult B: Mean = 106.5 m Standard deviation = 1.31 Compute the value of the test statistic (t):   |
|
Step 4: Make a
decision based on result |
Two-tailed test:Critical value tα/2 = ± 2.145 Use the t-distribution table to determine the critical value of tα or tα/2 Compare the values of test statistics, t, and critical value(s), tα or ± tα/2
 Therefore Ho rejected. |
|
Conclusion
that answer the initial question |
Since the test statistic t = 3.30 lies in the rejection region. The H0 is rejected. At 0.05 level of significance. Flying distance for catapult A produces a different flying distance of projectile as that of catapult B. |
|
Compare your
conclusion with the conclusion from the other team members. What
inferences can you make from these comparisons? |
The conclusion from other team member are different from what I get, their conclusion said that the catapult A and catapult B produces a same flying distance of projectile as that of catapult B. From these comparison with other member, It may because the data collected from run 8 is not very accurate. This can be due to many reason such as human error and enrioment factor. what can be improve to obtain a more accurate result is increase the number of data we collected. |
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