Hypothesis Testing

In this hypothesis testing entry, I got to be able to conduct hypothesis testing using values from my DOE practical. My groupmates from my DOE practical were:

1. Person A: Lionel Neo

2. Person B: Goh Wei Xue

3. Person C: Firmanshah Bin Bakhtiar

4. Person D: Anthony Lee Wen Rong

Firstly, lets take a look at our Full Factorial and Fractional Factorial method:

            Full Factorial Method

           Fractional Factorial Method

Lionel will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

Wei Xue will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

Firman will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

Anthony will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

Now, I (Firmanshah), will make use of the template table below to conduct the hypothesis testing for Run #5 for both Full and Fractional Factorial Methods.  

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 = 21.9 cm Start angle = 3 degree Stop angle =  High
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Catapult A produces the same flying distance of projectile as catapult B H0 : µ1=µ2 where µ1 is the theoretical value of flying distance by A                 µ2 is the theoretical value of flying distance by B   State the alternative hypothesis (H1): Catapult A does not produce the same flying distance of projectile as catapult B H1 : µ1 ≠ µ2 where µ1 is the theoretical value of flying distance by A                µ2 is the theoretical value of flying distance by B
Step 2: Formulate an analysis plan.	Sample size is 16, therefore t-test will be used.     Since the sign of H1 ≠ , a two tailed test is used.     Significance level (α) used in this test is 5%
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: Mean = 91.2cm Standard Deviation = 4.15 State the mean and standard deviation of sample catapult B: Mean = 87.3cm Standard Deviation = 2.89 Compute the value of the test statistic (t): Therefore test statistic value= 2.04
Step 4: Make a decision based on result	Type of test (check one only) Use the t-distribution table to determine the critical value of tα or tα/2 V= 14 α/2= 0.05/2=0.025 Therefore, confidence level = 0.975 From Distribution table,  tα/2= 2.145            Two-tailed test: [✅]  Critical value tα/2 = ± 2.145   Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 Using the two-tailed test, t=2.04 is within the acceptance range of the critical values, ±2.145. Therefore, H0 is accepted.
Conclusion that answer the initial question	At significance level 0.05, H0 is accepted where catapult A produces the same distance as Catapult B from Run 2. Thus, catapults A and B were manufactured consistently.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Comparing my conclusion to my groupmate's, it could be seen that all the test statistics values calculated by my groupmates fall within the range of critical values at different settings and at a significance level of 0.05.  Therefore, I can infer that for different settings but same significance levels at 0.05, h0 can be accepted. This means that the catapults we used during our DOE practical are manufactured consistently.

Learning Reflection

Through this hypothesis testing activity, I got to use statistical knowledge to conduct hypothesis testing on my DOE practical data. At the start of learning hypothesis testing, it was very overwhelming as I was not knowledgeable in statistics and all the key terms were all very new to me. It was very frustrating to understand it as well. However, during class, Mr Ting made the learning experience easy and I managed to understand hypothesis testing more clearly. The practice questions given in the learning package allowed me to make use of the equations used in hypothesis testing which helped me in this activity. This skill will definitely help me if hypothesis testing is needed for my FYP project in year 3. Before I am able to smoothly do that, I will need to do more practice on Hypothesis Testing calculations.