blog 5 (hypothesis testing)

Hi everyone, welcome back to my blog where today I will be telling you guys more about “hypothesis testing”!

In summary, hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.

The table below shows the data that we obtained from our DOE practical, where we made use of different factors to determine their significance against the distance travelled by the projectile. 

Since I am person C (Captain America), I will be using runs #2 and #6, to determine the effect of stop angle on the flying distance.

For Captain America, Black Widow. USE THIS TEMPLATE TABLE and fill all the blanks

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 =  ____cm Projectile weight = _____ grams Stop angle = _____ degree and ______ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): When a smaller stop angle is used, the distance travelled by the projectile will be the same as when a larger stop angle is used.      State the alternative hypothesis (H1): When a smaller stop angle is used, the distance travelled by the projectile will be greater than the distance travelled when a larger stop angle is used.
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 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 = 126.6 cm  Standard deviation = 1.10 cm     State the mean and standard deviation of Run #6: Mean = 87.2 cm  Standard deviation = 0.96 cm    Compute the value of the test statistic (t):   CL+SL = 1 CL = 1- 0.05 = 0.95
Step 4: Make a decision based on result	Type of test (check one only) 1.    Left-tailed test: [ __ ]  Critical value tα = - ______ 2.    Right-tailed test: [✓]  Critical value tα = 1.761 3.    Two-tailed test: [ __ ]  Critical value tα/2 = ± ______   Using the distribution table, when v = 14, t 0.95 = 1.761   When comparing the values of test statistics and critical values,  Since t > tα,  null hypothesis is rejected.
Conclusion that answer the initial question	Hence when a smaller stop angle is used, the projectile will travel a greater distance. However when a larger stop angle is used, the projectile will travel a shorter distance.
Compare your conclusion with the conclusion from the other team members.	Person A (Matthias): Using a lighter projectile leads to the projectile flying a larger distance while using a heavier projectile leads to the projectile flying a shorter distance. Person B (Eng Kiat): Person C (Sreenithi):  When a smaller stop angle is used, the projectile will travel a greater distance. However when a larger stop angle is used, the projectile will travel a shorter distance.   Person D (Abhishek):    Person E (Jun Yi): Using a lighter projectile will result in a larger flying distance of the projectile compared to using a heavier projectile
What inferences can you make from these comparisons?	I can infer that the lower the projectile weight, the greater the flying distance of the projectile. I can also infer that the lower the stop angle, the greater the flying distance of the projectile. Hence using LOW values instead of HIGH values, is going to give the greatest flying distance.
Your learning reflection on this Hypothesis testing activity	When I was first introduced to hypothesis testing, I was confused as to what its significance was to my course of study. After Mr Chua explained in depth what hypothesis testing meant, I could make more sense of its relevance to chemical product design. Initially, the concept of hypothesis testing was harder to grasp as compared to DOE because of technical terms such as null hypothesis, alternative hypothesis etc. Null hypothesis in summary indicates that differences in sample observations result purely from chance and that there is no statistically-significant difference in a set of given observations. However, alternative hypothesis indicates that differences in sample observations are statistically significant and influenced by some non-random causes. Until that day, when I thought about testing a hypothesis, I assumed that I had to carry out the experiment in order to see for myself if the experiment results align with my hypothesis. However, during that lesson I learnt that hypothesis testing could also be done by manipulating data that may be obtained from someone else doing the experiment. All I had to do was manipulate these data into the standard equations and determine their acceptance range using the different types of tests! It was a struggle to understand this concept as we had to be sure of when to use the different types of tests (right tailed, left tailed, two-tailed). Thankfully, we were provided with practice questions to attempt in order for us to grow more confident with this new skill! Mr Chua took his time to even go through an example to kickstart the problem solving session. After having attempted the practice questions, I can safely say that I have grown more confident with hypothesis testing. I look forward to applying this skill more in the future for my future experiments and internships as I feel that hypothesis testing is highly relevant in problem solving and experimentation! 😇😇