Hello everyone! Welcome to my fifth blog entry :D I rarely speak about things like this, but the past week had just been so stressful and hard to get through. Presentations, submissions, and assessments are coming up in the next one or two weeks, leaving my peers and I rather stressed out. Not to mention, we are currently experiencing a cold and rainy season, causing many of us to contract a cold...
I was having such a hard time, but thankfully, due to this blog entry, I am able to destress by sitting down at a corner of the school library and pouring out my thoughts about what I have learnt about Hypothesis Testing in my tutorial class, whilst applying it to the results from my practical session on Design of Experiment. I hope you enjoy reading this blog entry as much as I enjoyed writing it.
My group members from our Design of Experiment practical session were tasked to take on different roles of the Avengers, to allocate the runs that we will do hypothesis testing on, as shown below:
The runs are allocated so that each of us will do hypothesis testing on either the projectile weight or stop angle factor.
Before starting on the hypothesis testing, let me give you a run through of what Hypothesis Testing is!
Hypothesis Testing
Hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.
Hypothesis testing is used to answer questions such as:
Is the new material as strong as the old one?
Is the performance of our product enhanced after undergoing the revamp?
Does our product last longer than that of our competitors?
Is the new production process really faster than the existing one?
Is the spare part performing as well as the original part?
Did Class 2B09 really fare better in the MST than Class 2B08 did?
Iron Man and Batman. Who is more powerful?
Alright, that sums up my brief explanation of what Hypothesis Testing is! Let us start the testing...
The image below shows the experimental results from the Design of Experiment practical session:
Since I am Iron Man, I will be working on Run #1 & #3 to determine the effect of projectile weight on the flying distance of the projectile!
To determine the effect of projectile weight 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 projectile.
Flying distance for catapult is collected using the factors below:
Arm length = 28.1 cm
Projectile weight = 0.86 grams and 2.87 grams
Stop angle = 50 degree
Step 1: State the statistical hypothesis
State the null hypothesis (H0):
The distance travelled by the projectile will remain unchanged when the projectile weight is increased from 0.86 g to 2.87 g, while the arm length and stop angle remains constant.
State the alternative hypothesis (H1):
The distance travelled by the projectile will decrease when the projectile weight is increased from 0.86 g to 2.87 g, while the arm length and stop angle remains constant.
Step 2: Formulate an analysis plan
The sample size is 16. Therefore, the 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 4: Make a decision based on the results
Type of test (check one only)
1. Left-tailed test: [ ✓ ]
2. Right-tailed test: [ __ ]
Critical value tα= ______
3. Two-tailed test: [ __ ]
Critical value tα/2= ± ______
v = n - 1
= 8 -1
= 7
Since α = 0.05,
t1 - 0.05 = t0.95
At v = 7 & t0.95,
Critical value tα= - 1.895
By comparing the values of test statistics, t, and critical value, tα,
t = - 3.16
tα = - 1.895
It is concluded that H0 is false as the test statistic t = - 3.16 lies in the rejection region.
Conclusion that answers the initial question :>
Since H0 is false, H1 will be true.
In other words, it is true that the distance travelled by the projectile will decrease when the projectile weight is increased (from 0.86 g to 2.87 g), while the arm length and stop angle remains constant.
Comparing my conclusion with the conclusion from my other team members...
Myself: Iron Man (Run #1 & #3)
The distance travelled by the projectile will decrease when the projectile weight is increased (from 0.86 g to 2.87 g), while the arm length and stop angle remains constant.
The distance travelled by the projectile will decrease when the projectile weight is increased (from 0.86 g to 2.87 g), while the arm length and stop angle remains constant.
Brice: Captain America (Run #2 & #6)
The distance travelled by the projectile will decrease when the stop angle is increased (from 50 to 70 degrees), while the arm length and projectile weight remains constant.
Jian Ye: Black Widow (Run #4 & #8)
The distance travelled by the projectile will decrease when the stop angle is increased (from 50 to 70 degrees), while the arm length and projectile weight remains constant.
The distance travelled by the projectile will decrease when the projectile weight is increased (from 0.86 g to 2.87 g), while the arm length and stop angle remains constant.
Inferences I made from these comparisons
From comparing the conclusions by my group and observing the trends, I can infer that:
The distance travelled by the projectile will decrease when the projectile weight is increased (from 0.86 g to 2.87 g), while the arm length and stop angle remains constant.
The distance travelled by the projectile will decrease when the stop angle is increased (from 50 to 70 degrees), while the arm length and projectile weight remains constant.
My learning reflection on this Hypothesis Testing activity~
To be honest, I expected my Design of Experiment blog to be the last time I would ever hear about Design of Experiment in this module. To my surprise, Hypothesis Testing is also related to it. I never expected to see the experimental results from the Design of Experiment practical again. To be able to apply what I learnt from Hypothesis Testing on it felt very surprising and cool to me. It is yet another instance where I realise that everything we learn is connected and have correlations with each other, and that just feels so surreal to me.
Other than how I feel, let me discuss about my reflection on Hypothesis Testing.
I recall my first tutorial lesson on Hypothesis Testing, where my classmates and I spent hours completing a list of questions regarding Hypothesis Testing. It was really tedious for us, as there were new sets of equations and theories to learn about. We were supposed to complete the questions and submit it by the end of the tutorial lesson, but I was unable to because I just could not understand the theory behind Hypothesis Testing. I could only follow the steps in the first question, where the workings and answer were provided, for all the other questions. However, completing this blog on Hypothesis Testing turned out much easier than completing the questions, as I have already practised doing Hypothesis Testing through the questions. It was much easier to understand the workings invovled now that I look at it again so that I could complete this blog entry. I guess we can say that the list of questions were a blessing in disguise...
I also recall writing hypotheses multiple times throughout my primary and secondary school studies. It was much simpler than now, as we just had to write a hypothesis guess, complete an experiment, observe the results and write if the hypothesis is true or not based on the final result we gained from the experiment. There were no testing, equations, or theory involved. If the experiment results matched with the hypothesis, we would just say that the hypothesis is true. Due to this, learning about Hypothesis Testing now is truly mind-blowing to me because of all the equations and workings behind it. I would have never expected that proving a hypothesis true or false could be so tedious. However, I understand the significance behind it, as it is a more reliable framework for proving hypotheses.
In conclusion, I would like to express how glad I am to have learnt about Hypothesis Testing. It surely will turn out useful in the future, especially in my upcoming Final Year Capstone Project.
With that, my second last blog entry comes to an end! See you again soon in my last blog entry... about the development of my prototyping project on a self-sterilising door handle!
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