Hypothesis Testing

Hi guys, welcome back to a new blog! This blog is closely related to the previous blog I uploaded about DOE, I hope you guys read that! Anyway, this blog will be about a new topic, hypothesis testing... And honestly I'll just be sharing about an example I'll be doing as Captain America!! (According to the template given) Before we begin, you may first want to read about what exactly is a hypothesis! A hypothesis is an assumption about a population parameter, which may or may not be true. It refers to procedures used by researchers to accept or reject statistical hypotheses.

With this, I will be using runs #2 and #6 to determine the effects of stop angle.

The QUESTION	To determine the effect of stop angle on the flying distance of the projectile.
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 is collected using the factors below: Arm length =  33 cm Projectile weight = _0.8_ grams 0% infill density Stop angle = _45_ degree and _95_ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The high stop angle (+) and the low stop angle (-) generates the same flying distance of projectile.  μ=μ0 State the alternative hypothesis (H1): The high stop angle (+) and the low stop angle (-) generates different flying distance of projectile. μ≠μ0
Step 2: Formulate an analysis plan.	Sample size is less 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 Run # 2: Mean(X1) : 94.3 Standard Deviation(S1): 2.87 State the mean and standard deviation of Run #6: Mean(X2) : 90.3 Standard Deviation(S2): 2.99 Compute the value of the test statistic (t): n(1)=n(2)=4 v=6 σ= 3.38 Test statistics (t)=1.67
Step 4: Make a decision based on result	Type of test: Two-tailed test Critical value tα/2 = t(0.0975) = ± 2.447 Use the t-distribution table to determine the critical value of tα or tα/2 Since t=1.67, which is in the acceptable region, therefore null hypothesis (Ho) is accepted.
Conclusion that answer the initial question	Since null hypothesis is accepted, it meant that the high stop angle (90 deg) and the low stop angle (45 deg) generates the same flying distance of projectile  μ = μ0 I can conclude that stop angle does not have a significant effect on flying distance of projectile.
Compare your conclusion with the conclusion from the other team members.	Here are the compiled results from the rest if my groupmates: Jing Yue (Iron Man): Runs 1 and 3 His results shows that using 0.86g projectile weight and 2.08g projectile weight have significant effect on the flying distance of the projectile. Yu Jie(Thor): Runs 2 and 4 His results are the same as Jing Yue, where using 0.86g projectile weight and 2.08g projectile weight have significant effect on the flying distance of the projectile. Dhasna(Black Widow): Runs 4 and 8 Her results shows the same as mine where stop angle does not have a significant effect on flying distance of projectile!
What inferences can you make from these comparisons?	I can infer that, 1. projectile weight gives a more significant effect on the flying distance of the projectile weight 2. stop angle does not give significant effects on the flying distance of the projectile weight This can be proven by the findings my group have made, where both jingyue and yu jie, by comparing 2 different runs produced the same findings and same for me and dhasna!
Your learning reflection on this Hypothesis testing activity	To be very honest, when Mr Chua was teaching this topic, I was unwell and absent for his class...HOWEVER before anyone marks me down, I worked very hard to stay on track and even asked many of my classmates questions whenever I didn't understand anything on the slides. Lucky for me I had a friend taking a module called quality assurance and statistics, and they learnt hypothesis testing as a whole topic! So he really helped me out this time. But even so, I found this topic quite dry and didn't really understand why we had to learn it.... it was only after practical 3 where I realised how important hypothesis testing is to really get reliable results that could prove a study! I also started to get better understandings after doing afew practise questions and finally got the hang of it by the last few questions! I realised how having this skill, just like DOE will be very handy for my Final Year Project!

Alright, that will be all for this blog! I hope this table helped you guys better understand what hypothesis testing is and what it is useful for! My next blog will be about a very fun project my group mates and I have been working on for quite some time now, I hope you guys are just as excited for that:)