Hypothesis Testing

In this blog, I will be documenting on the hypothesis testing task that was given for our individual blog. It was based on the Design of Experiments (DOE) practical. In the DOE practical, we made use of two catapults, one for full factorial design and the other for fractional factorial design. In this blog, I will be doing the hypothesis testing on the results that we have collected during the experiment. 

These are the team members from the DOE practical:

1. Steward (Iron Man)

2. Wayne (Thor)

3. Jiayu (Captain America)

4. Xinni (Black Widow)

5. Nick (Hulk)

6. - (Hawkeye)

Roles for each character: 

1. Iron Man will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

2. Thor will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

3. Captain America will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

4. Black Widow will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

5. Hulk will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

6. Hawkeye will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

Since I have chosen the Iron Man character, I will be using Run#2 from both the fractional and full factorial designs.

Data collected for FULL factorial design using CATAPULT A:

Data collected for FRACTIONAL factorial design using CATAPULT B: 

Using the template provided:

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 the projectile. Flying distance for catapult A and catapult B is collected using the factors below: Arm length = 32cm Start angle = 0 degree Stop angle = 55 degrees
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Catapult A and catapult B produces the same flying distance of the projectile. μA = μB State the alternative hypothesis (H1): Catapult A and catapult B produces different flying distance of the projectile. μA ≠ μB
Step 2: Formulate an analysis plan.	Sample size is 8, which is less than 30. Therefore, t-test will be used. Since the sign of H1 is ≠, so a two tailed test is used. Significance level (α) used in this test is 0.05, because this is usually the default used for significance level.
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: State the mean and standard deviation of sample catapult B: Compute the value of the test statistic (t):
Step 4: Make a decision based on result	Type of test (check one only) Left-tailed test: [ __ ]  Critical value tα = - ______ Right-tailed test: [ __ ]  Critical value tα =  ______ 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, since t = -1.007 lies in the acceptance region, Ho is accepted.
Conclusion that answers the initial question	It can be concluded that the products they manufactured are consistent and up to standard when the significance level (α) is 0.05.
Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?	The conclusion gathered from other team members is that the products that were manufactured were consistent. At significance level of 0.05, both catapults will produce similar distance. It can be inferred that from these comparisons, at different settings of the catapult, the catapults are still consistent in the distance which the projectile flies.

Reflection:

In this hypothesis testing learning experience, during the lesson, our lecturer went through the slides and introduce hypothesis testing to us. I tried to understand and learn as much as possible. However, I still have some parts that I don't understand. After the lecture, we were tasked to do some practice questions. The practice questions were quite challenging because of my lack of experience and understanding. I get to learn as I do the questions by looking through the slides and clarifying any doubts with the lecturer, from this experience, I've gained a better understanding of hypothesis testing. Once I got the hang of it, and I understood the steps on hypothesis testing, I feel that it is not too hard to do. I feel that this skill will be useful when doing experiments for the final year project. This could even be beneficial after I graduated. I used to think that this hypothesis testing method is difficult and kind of pointless because I don't fully understand the use for it. After completing the hypothesis testing practice questions and the task for this blog, I now know the uses of this hypothesis testing method, and I know that it could be very useful for other applications.