Hypothesis Testing

In this practical, we had carried up an experiment that was related to Design of Experiment, which we had to use a catapult to launch the projectile with certain aspects.

For this practical, there are several factors that will affect the distance of the projectile landed which showed in the image below. After the testing, we competed with other groups in our class to determine which groups' projectile was able to hit the target.

Group 2:

1. Tan Junheng

2. Haziq

3. Ambrose (me!!!)

4. Zelene

5. Zhi Wei

Data collected for FULL factorial design using CATAPULT A :

Data collected for FRACTIONAL factorial design using CATAPULT B :

After a short discussion with my team members, I am assigned to use Run #3 from Fractional factorial and Run #3 from Full Factorial.

Here are the guides from the tutorial slides which will enable me to recap what I had learned during the tutorial:

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 =  23.5   cm Start angle =   +20    degree Stop angle =    -49    degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The distance landed by the projectile after launching using catapult A is the same as using catapult B. State the alternative hypothesis (H1): The distance landed by the projectile after launching using catapult A is different with using catapult B.
Step 2: Formulate an analysis plan.	Sample size is    8     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 = 155.3 Standard deviation = 4.07 State the mean and standard deviation of sample catapult B: Mean = 151.9 Standard deviation = 2.77     Compute the value of the test statistic (t): Sample means: x̄1 = 155.3 x̄2 = 151.9 Sample sizes: n1= 8 n2= 8 Standard deviation of the samples: s1= 4.07 s2= 2.77 v = n1 +n2 -2    = 8 +8 -2    = 14 Since we are comparing two samples, to calculate σ, use the formula: σ = √ ( (8 x (4.07)^2) + (8 x (2.77) ^2)  / 14 )    =  3.72 To calculate t,  use the formula:   t = (155.3 - 151.9) / 3.72 √ 1/8 +1/8   = 1.83
Step 4: Make a decision based on result	Type of test (check one only) 1.  Left-tailed test: [ __ ]  Critical value tα = - ______ 2. Right-tailed test: [ __ ]  Critical value tα =  ______ 3. Two-tailed test: [ ✔ ]  Critical value tα/2 = ± 2.145 Use the t-distribution table to determine the critical value of tα or tα/2 Since v=14, t±0.975 = 2.145 Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 t= 1.83, t0.975 = 2.145 t= -1.83, t0.975 = -2.145 Since t lies on the acceptable region of t±0.975 = 2.145 Therefore Ho is acceptable    .
Conclusion that answer the initial question	The distance landed by the projectile after launching using catapult A is the same as using catapult B.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	After comparing my conclusion with my team members, majority of my team members' conclusion are null hypothesis is accepted, whereas alternative hypothesis is rejected. From our group's conclusion, the distance landed by the projectile after launching using catapult A is the same as using catapult B.

Individual Reflection:

In this practical, I have learnt about how hypothesis testing can really impacts our progress of the catapult to launch the projectile. This practical is important because we are going to make use of what we have learned in this practical in our prototype, possibly the capstone project for next year. What makes the tasks interesting is that I am able to experiment the catapult with different factors such as change the wood launcher with the 3D printed launcher to launch the projectile, changing the start angle and stop angle to determine which factors can allows the projectile to land further.

I used to think that hypothesis testing is useful for almost every project because it can helps us to obtain better results after several runs by changing the factors, then continue to run the tests. So next, I will make use of what I have learned in this hypothesis testing in my final year project, or even the prototype that we are going to present on Week 18.