Hope everyone is doing well despite this term's insane timetable:/ It has been crazy since every week seemed like its always crunch time where assignments has to be rushed and our sleep time to be sacrificed😖. However fret not! We are on our last stride of this semester just remember to repose and rest to tackle our last 2 weeks of school👍.
Today I will be sharing something interesting yet mysteriously difficult to grasp:)
Hypothesis testing
So... What is this hypothesis testing thing I have mentioned?
It it actually some atas procedure used to deduce whether do accept or reject a statistical claim. It is one of the best ways to establish if a statistical hypothesis is true with a fraction of the total size when conducting an experiment!
Then, why is it useful?
In real world, the pleasure of determining how true a hypothesis is with a full strength of data is nearly impossible due to many retrains such as economical cost and duration, hence we have to make many smaller sample test to see if the statistical hypothesis of something is true.
In today's blog my team and I will show u a hypothesis testing on our previous catapult experiment/game that we enjoyed. Each of my teammate has chosen to fulfill a duty of being an avenger for this segment of the term to see who is the most powerful avenger.
In this case my group did a mystery draw and this was the outcome:
1. Iron man - Diana
2. Thor - Shaira
3. Captain America - Qian yu
4. Black widow - Sanjana
5. Hulk - moi
From this draw we already know who is going to smash this competition:)
This is the data for the catapult experiment
The Question:
Determine the effect of the Projectile weight on the flying distance of the ball projectile.
The scope of the test:
Flying distance for the catapult is collected using the factor below
Arm length= 33cm
Projectile weight= 0.85grams and 2grams
Stop angle= 140degree
The human factor in this experiment is assumed to be negligible, therefore different user have no effect on the flying distance of the ball projectile.
Step 1: State the statical hypothesis:
The null hypothesis (H₀):
When the arm length is constant at 33cm and stop angle at 140 degree, the flying distance of the ball projectile with 0.85grams has the same result as the ball projectile that is 2grams.
𝜇6=𝜇8
The alternative hypothesis (H₁):
When the arm length is constant at 33cm and stop angle at 140 degree, the flying distance of the ball projectile with 0.85grams has a smaller result as compared to the ball projectile that is 2grams.
𝜇6>𝜇8
Step 2: Formulate an analysis plan.
Sample size is 16, therefore t-test will be used.
Since the sign of H₁ is >, a right tailed test will be used.
The significance level (α) used in this test is 0.05
Step 3: Calculate the test statistic.
For Run #6
x̅ (mean) = 93.1
s (standard deviation) = 3.89
For Run #8
x̅ (mean) = 90.2
s (standard deviation) = 3.99
Step 4: Make a decision based on results
Type of test (check one only)
1. Left-tailed test: [ ✔️ ] Critical value tα = __1.761__
2. Right-tailed test: [ ] Critical value tα = ____
3. Two-tailed test: [ ] Critical value tα/2 = ± ____
By comparing the statistic, since the rejection area is 1.761 and above , t=1.377,
t lies in the acceptance region and hence the null hypothesis (H₀) is accepted at the significance level (SL) of 0.05.
Conclusion to the initial question
As t0.95= -1.761, our t value is accepted and this means that at a SL of 0.05, the null hypothesis is accepted and the answer is null hypothesis. This means with a higher weighted 2grams projectile has a similar flying distance compared to the lower weighted 0.85 gram projectile at a significance level of 0.05.
Comparing my conclusion with other avengers in
Iron man - Diana
From the graph, Factor C (power) is the most influential factor as it has the largest gradient, followed by B and then A.
Thor - Shaira
The distance travelled by the projectile will increases when the projectile weight is increased (from 0.85 g to 2g), while the arm length and stop angle remains constant.
Captain America - Qian yu
With a constant arm length of 33cm and a constant projectile weight of 0.85g, the flying distance of projectile using 140 degree and 190 degree will yield different results.
Black widow - Sanjana
What inference I can deduce from these comparisons
My learning reflection 🔨🔪🪚
During the tutorial lessons I recalled how bamboozled I was. It was utter chaos especially the addition of newly seen symbols that felt like parasites in my brains. The formulas seemed alien and still the thought of it makes my stomach crumble. The overwhelming sensation of learning this mathematic/data statistic felt as though it was acid spraying on top of my head which melted my brains away.
It was a monday morning and I was full of energy when I came to class, after an hour into the class I was as confused as a baby leaning how to speak. It was not just me as I observed the class, my classmates were either frowning, busy trying to figure out what is happening and some who have already given up. Even Mr Chua our lecturer was having trouble understanding it let alone explaining it to us in the first while.
However... after sometimes! I still can't understand it so I had to ask around for people who could understand and hope they are willing to share their mind-bloggling discovery.
Prior to learning hypothesis testing for statistical data I always thought because hypothetical statements can be easily given by anyone, the testing of these hypothesis should also be an easy task that everyone can do. Boy was I wrong to provide an evidence to support a hypothesis goes deep and require many testing and retesting which was exposed to me during the making of this blog.
From this lesson activities I have actually found out and appreciate the details that goes into proving and supporting a hypothesis. The act of hypothesizing is easier said then done especially after seeing how many runs we have to do to have a valid conclusion. An example will be how a team of avengers are needed to prove the hypothesis validity. This journey has been extremely confusing and I do believe there are better ways to tackle this lesson or this idea of hypothesis testing.
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