Blog Entry 5: Hypothesis Testing

Welcome back everybody! In this blog I will be talking about hypothesis testing and sharing everything that I have learned. 

HYPOTHESIS TESTING

The first thing we should know about is what exactly is hypothesis testing. While it may seem quite obvious from the name itself, it is actually much deeper than what I thought it would be.

Hypothesis testing allows for statistical hypothesis to be proven or rejected through formal procedures.

Statistical hypothesis: an assumption about a population that may or may not be correct.

Hypothesis testing can be 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?
• Is the spare part performing as well as the original part?

In my case I will be conducting an experiment to undergo hypothesis testing for the effects of various factors on a catapult. Frequent readers of my blog will recognise that this is actually the same experiment as my practical for Design Of Experiment.

Conducting The Hypothesis testing

For this experiment, my CPDD practical group have been split into different roles and we will each be conducting hypothesis testing on each of our allocated runs.

Here are our roles and responsibility:

Name of heroes (students)	Runs	Factor tested
Ironman (Jia Tong)	#1 & #3	Effect of projectile weight
Thor (Devin)	#2 & #4	Effect of projectile weight
Captain America (Jun Kai)	#2 & #6	Effect of stop angle
Black Widow (Aminur)	#4 & #8	Effect of stop angle
Hulk (Ji Hinn – Me)	#6 & #8	Effect of projectile weight

After allocating our roles, we then proceeded to conduct hypothesis analysis using the data we collected before:

I will be using the data for run #6 and #8 and following the formal procedures to conduct hypothesis!

The Question

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 user will not have any effect on the flying distance of projectile.

Flying distance for catapult is collected using the factors below:                                              Arm length = 33 cm                                                                                                                    Projectile weight = 0.88 grams (run #6) and 2.07 grams (run #8)                                              Stop angle = 50 degrees

Step 1: State the statistical hypotheses

Null hypothesis (H₀): When the arm length and stop angle of the catapult remain constant at 33 cm and 50 degrees respectively, the distance travelled for projectile weight of 0.88 grams will be the same as a projectile weight of 2.07 grams. 

µ^­­₆ = µ^­­₈   

Alternative hypothesis (H₁): When the arm length and stop angle of the catapult remain constant at 33 cm and 50 degrees respectively, the distance travelled for projectile weight of 0.88 grams will be further than a projectile weight of 2.07 grams.

µ^­­₆ > µ^­­₈   

Step 2: Formulate an analysis plan

Sample size is 16. Therefore, t-test will be used.

Since the sign of is H₁  >, a right-tailed test is used.

Significance level (α) used in this test is 0.05

Step 3: Calculate the test statistic

Mean and standard deviation of run #6    

X̄₆ = 196.00 cm                                                                                                                    

S₆  =  4.11  cm

Mean and standard deviation of run #8

X̄₈  = 174.75 cm

 S₈  = 2.87 cm

Computing the value of test statistic (t):

Step 4: Make a decision based on result

Type of test

1. Left-tailed test [ ], Critical value t_α  = 
2. Right-tailed test [✔], Critical value t_α = 1.761
3. Two-tailed test [ ], Critical value t_α/2  = 

Finding t_α

Following the diagram above, since t = 11.3 and t_α = 1.761, t > t_α. Therefore, t lies within the rejection area and H₀ is rejected.

Conclusion

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.

Comparing conclusions

Ironman (Jia Tong): When the projectile weight is lighter, the flying distance will be longer.

Thor (Devin): Using a lighter Projectile Weight of 0.88grams 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): 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 (Me): 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.

Please check out my groupmates' blogs too! Links to all my groupmates' blogs:

Ironman (Jia Tong)

Thor (Devin)

Captain America (Jun Kai)

Black Widow (Aminur)

Inferences made from conclusions

Weight of projectile have an effect on distance travelled

• The lower the weight of projectile, the longer the distance travelled

Stop angle have an effect on distance travelled

• The greater the stop angle, the longer the distance travelled

Learning Reflections

I was first introduced to the term hypothesis by my teacher in secondary school years ago. I had always thought that hypothesis is a simple matter of conducting an experiment for data to prove or disprove the hypothesis. However, I was proven wrong by my teacher during the lesson on hypothesis testing. 

To my surprise hypothesis is much deeper than what I thought. This just shows that there is still a lot of things I do not know and can learn about! I was introduced to a procedure that guided me on how to conduct hypothesis testing. This is the same procedure as the one I used in my experiment above! In the procedure, there were a lot of new symbols and equations that I have never seen before. I was quite worried that I would have to memorise them but thankfully that was not needed.

Despite being overwhelmed at first, as I practiced using the procedure I realised how impressive it was. For example, using the procedure allows comparison between two samples instead of testing a single sample. This opens new opportunities on how I can utilise hypothesis testing. I could remember clearly how I felt I was improving as I practiced using the procedure for the practice questions. So it is extremely rewarding to learn. 

Overall this have been an extremely fun and useful topic that I have learnt. I looked forward to being able to use the procedure again. I am extremely thankful to my teachers and fellow groupmates for accompanying me through this topic.

Thank you for reading until this point, I will be stopping now as its been quite long. please look forward to my next blog! Bye!!