Hey guys...
I've been feeling absolutely burnt out these past few days and haven't had the mood to do anything. The weirdest part is that I don't feel stressed and I'm numb to feelings such as fear, sadness and regret. If Polytechnic already feels like hell, University must feel like dying in agony and coming back to life and dying again in an eternal cycle of pain. At least through this journey in SP, I discovered that I had a hidden interest within me in product design and development. Hence, I'll be sharing a unique skill I recently learnt about hypothesis testing.
First things first, what is hypothesis testing?
Hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses. The ideal way to determine if a statistical hypothesis is true is by examining the entire population. Since that is often impractical, researchers usually examine only a random sample from the population. If the sample data is not consistent with the statistical hypothesis, the hypothesis is rejected.
My CPDD practical groupmates and I will be collaborating in our own personal blogs to show the reliability of hypothesis testing by conducting hypothesis testing on the catapult practical we completed a few weeks ago. Each of us has been assigned an Avengers character to complete a mission. Each Avenger must conduct hypothesis testing using different runs we did for our Full Factorial experiment design. The following shows the runs each Avenger must use for their hypothesis testing:
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 users will not have any effect on the flying distance of the projectile. Flying distance for the catapult is collected using the factors below: Arm length = 33 cm Projectile weight = 2.08 grams Stop angle = 30 degrees and 50 degrees
Step 1: State the statistical hypothesis
State the null hypothesis (H0): When the arm length is 33 cm and the projectile weight is 2.08 grams, the distance travelled by the projectile using a stop angle of 30 degrees and 50 degrees will have no difference.
𝜇4 = 𝜇8
State the alternative hypothesis (H1): When the arm length is 33 cm and the projectile weight is 2.08 grams, the distance travelled by the projectile using a stop angle of 30 degrees will be lower than using a stop angle of 50 degrees.
𝜇4 < 𝜇8
Step 2: Formulate an analysis plan
Sample size is 16 Therefore t-test will be used.
Since the sign of H1 is < , a left-tailed test is used.
Significance level (α) used in this test is 0.05
Step 3: Calculate the test statistic
Step 4: Make a decision based on the result
Significance Level (SL/α) = 0.05
Confidence Limit (CL) = 0.95
v = 14
Type of test: 1. Left-tailed test: [✔️] Critical value tα= - 1.761 2. Right-tailed test:[ __ ] Critical value tα= _____ 3. Two-tailed test:[ __ ] Critical value tα/2= ±___
Since t < tα, the test statistic, t = -17.8145 lies in the rejection region. Hence, the null hypothesis (H0) is rejected at a significance level of 0.05
Therefore, H0 is false.
Conclusion that answers the initial question
When the arm length is 33 cm and the projectile weight is 2.08 grams, the distance travelled by the projectile using a stop angle of 30 degrees is lower than using a stop angle of 50 degrees.
Comparing my conclusion with the conclusion of the other Avengers
Iron Man: Jia Tong When the projectile weight is lighter, the flying distance will be longer.
Thor: Devin Using a lighter Projectile Weight of 0.88 grams will result in a further flying distance travelled by the projectile.
Captain America: Jun Kai Using a bigger stop angle would result in a larger flying distance of the projectile while using a smaller stop angle would result in a smaller flying distance of the projectile.
Black Widow: Aminur [Me, Myself & I] When the arm length is 33 cm and the projectile weight is 2.08 grams, the distance travelled by the projectile using a stop angle of 30 degrees is lower than using a stop angle of 50 degrees.
Hulk: Ji Hinn When the arm length and stop angle of the catapult remain constant at 33 cm and 50 degrees respectively, as the projectile weight decreases from 2.07g to 0.88g the distance travelled increases. (Hulk has gotten out of control and hasn't returned to the hideout yet. I'm currently trying to find him in the amazon jungle to calm him down. I think he might have a crush on me...)
Inferences I made from these comparisons
The flying distance of our projectile increases as the weight of the projectile decreases.
The flying distance of our projectile increases as the the stop angle increases.
Learning Reflection
I would've never thought that testing if a hypothesis was true or false could be so long and tedious. I believed anyone could conclude if their hypothesis was true or false by simply glancing at their experimental data. However, if I imagined myself as an engineer working on a complicated product, it could be quite difficult for the team to make a rational conclusion especially if the experimental data was scattered everywhere. Hence, having a step-by-step method to determine if a hypothesis could be true or false is very convenient.
I could vividly recall that I was extremely lost when Mr Chua was going through the steps to conduct hypothesis testing. I asked around for help but I still couldn't understand anything. Hence, I utilised the greatest skill in my inventory which I have been developing for the past 6 years of my life, "the art of bullshiting". With this skill, the class activity became as easy as baking a cake. I didn't understand what I was doing, but following the steps stated in the slides was sufficient enough to complete the questions we were tasked to solve by the end of the lesson.
However, after revisiting hypothesis testing for this blog, I ACTUALLY FINALLY UNDERSTAND THE PURPOSE OF EACH STEP. Hypothesis testing is actually much simpler than expected as we just have to understand what each step wants us to solve or identify which makes the lives of us busy engineers a little bit easier.
I can see myself using the skills I've learnt from Design Of Experiments and Hypothesis Testing in my Final Year Project in the following semester. I recall that during the lesson, Mr Chua mentioned that in the past, a GPA 4.0 student manipulated her SL value to be more than 0.05, which shouldn't be done. Instead, we should manipulate our values and stick to an SL value of 0.05 to stay true to the hypothesis testing method. Other than that, I feel mentally prepared for my FYP project from all the hands-on practicals I've completed in the past 2 years. I just hope that my groupmates can come up with an interesting topic to tackle so that we can stand out from the crowd.
----------This marks the end of this week's blog, and you'll see more of me in 2 weeks-----------
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