Hypothesis testing
For this assignment, I will use the DOE experimental data that my practical team have collected both for FULL Factorial and FRACTIONAL Factorial.
DOE Practical Team Members:
- Heng Leon
- Rufus How
- Sean Tay
- Ethan Chan
- Alton Yau
Data collected for FRACTIONAL factorial design using Catapult B
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:
The human factor is assumed to be negligible. Therefore, different users will not have any effect on the flying distance of the projectile.
Flying distance for catapult A and catapult B is collected using the factors below
[Factor A] Arm length = __ cm
[Factor B] Start angle = __ degree
[Factor C] Stop angle = __ degree
Step 1: State the statistical hypotheses
H0: Catapult A has the same flying distance of projectile as that of Catapult B. μ1=μ2
H1: Catapult A does not have the same flying distance of projectile as that of Catapult B. μ1≠μ2
Step 2: Formulate an analysis plan
The sample size is 16, 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 5%.
Step 3: Calculate the test statistic
Using runs #5 for both Full and Fractional Factorial,
For CATAPULT A:
Mean = 87.7
Standard Deviation = 4.39
For CATAPULT B:
Mean = 105
Standard Deviation = 6.03
Computing of test statistics:
v = 8 + 8 + 2 = 14
At significance level of 5%,
Area = 1 - (0.05/2) = 0.975
From the Student's Distribution Table,
At t,0.975 and v = 14,
t = ±2.145
Since t-test value falls outside the acceptance region of t = ±2.145, Ho is rejected
This means that at a significance level of 5%, Catapults A & B does not give the same flying distance for the projectile. Thus, the manufacturer is not consistent.
Compared with the results of my groupmates, the same conclusion can be drawn, that the catapults do not give the same flying distance and the t-test values fall in the rejection region despite the different levels of significance used. This shows that the significance level only affects the regions slightly and the catapults manufactured are not consistent.
Reflection
This week's practical really opened my mind to new ways to test for hypothesis. However, I am still new to this and I still get confused on how to do the proper steps, but I think that with more practice, I will definitely improve and be more competent in doing hypothesis testing.