HYPOTHESIS TESTING

 HELLO👋 and welcome back to another blog. This week we would be looking into hypothesis testing using our full and fractional factorial we have found during our practical. There are 3 factors we would be looking at. they are the stop/start angle and the length of the arm.

DOE practical team members:

1. Kalyani(me)

2. Jolyn

3. Brayden

4. Gideon

DATA COLLECTED FOR FULL FACTORIAL USING CATAPULT A:

DATA COLLECTED FOR FRACTIONAL FACTORIAL USING CATAPULT B:

KALYANI(ME) will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.

JOLYN will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

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

GIDEON will use Run #6 from FRACTIONAL factorial and Run#6 from FULL factorial.

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 =  30.5cm Start angle = 20 degree Stop angle = 60 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): This means that there will not be any effect on the flying projectile. μA = μB     State the alternative hypothesis (H1): This means it will have an effect on the flying projectile.  μA ≠ μB
Step 2: Formulate an analysis plan.	Sample size is 8 which is lesser than 30. 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: 98.8 standard deviation:14.38     State the mean and standard deviation of sample catapult B:  mean:127.9 standard deviation: 3.83     Compute the value of the test statistic (t): T0.975 , V= 14, boundary t =2.145
Step 4: Make a decision based on result	Type of test (check one only)           T0.975 , V= 14      Critical value tα/2 = ± 2.145     since t=-5.17,Therefore Ho is rejected.
Conclusion that answer the initial question	In conclusion, seen from the above results, different users has an effect on the flying arm of the projectile.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Catapult A and catapult B are not being consistent in terms of manufacturing. They are different, hence causing different results. therefore manufacturing are not up to standard. I can infer that one of the aspects which affected the flying projectiles, is the tension of the rubber bands. Some may be weaker while some maybe stronger which causes the difference in the flying projectiles. another aspect is that catapult A's start angle was way more tilted compared to catapult B's start angle. Therefore the distance may have been affected as there will be more force in one catapult compared to another.

Reflection:

When I first saw hypothesis testing, i thought it was gonna be easy and it was just all about making a hypothesis and justifying it with explanations. But I got to know that there is more to it such as calculations. I was actually pretty clueless and i had to always look at the slides to try and understand the exercises before the lesson starts. after the lecturer went through the topic with us it became more clearer, and I was able to do the work more smoothly. hence it was even more benefitting, as I was able to implement this texting on a real life practical I had done before. This was something fruitful to learn about and I am pretty sure I will be able to use this for my upcoming projects.