HYPOTHESIS TESTING

Welcome back! In this blog, I will be doing hypothesis testing on the results from my group's runs during the DOE practical (remember?😶) 

Before we get into it, what is hypothesis testing? 😱

It is an assumption about a population parameter. However, this assumption may or may not be true. Hypothesis testing refers to the formal procedures used by experimenters or researches to accept or reject a hypothesis. A sample of a population is used to estimate the results produced by a population, as examining an entire population is often impractical. 

In the case of our DOE practical, we are using hypothesis testing to see if the different parameters (projectile weight or stop angle) has a significant effect on the flying distance of the projectile! Afterwards, we can either reject or accept the null hypothesis. 

My team members: 

En ting (Captain America) 

Justin (Thor) 

Keith (Hulk) 

Jun Hao (Black widow) 

 Me (Hannah): Iron Man🤖

Iron Man will be using Run #1 and Run #3 to determine the effect of the projectile weight 

Full factorial results obtained from my group: 

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 =  __12.5__cm Projectile weight = ____0.86_ grams and _2.05_____ grams Stop angle = ___49_ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The projectile weight has no significant  effect on the flying distance of the projectile.  State the alternative hypothesis (H1): The projectile weight has an significant effect on the flying distance of the projectile.
Step 2: Formulate an analysis plan.	Sample size is ___8_ Therefore t-test will be used.     Since the sign of H1 is _±___, a two- 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 # _1_: Mean = 152.8cm  Standard deviation = 4.56  State the mean and standard deviation of Run #_3_: Mean = 127.4cm  Standard deviation = 5.83cm  Compute the value of the test statistic (t): X is the mean of sample (X1 = 152.8cm, X2 = 127.4cm)  population size = 64 n is the sample size (n=8, since there were 8 runs being carried out) n1 = n2 = 8 𝝈 is the standard deviation of the population  s is the standard deviation of the sample  s1 = 4.56cm , s2 = 5.83cm v is the degree of freedom  v= n1 + n2 - 2 = (8+8)-2 = 14 1. Calculate 𝝈:  𝝈 = √[(8)(4.56)^2 + (8)(5.83)^2] ÷ [14]      = 5.595  2. Calculate t:  t = [152.8 - 127.4] ÷ 5.595 [√ (1/8) + (1/8)]    =±9.0795
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 =  ______ 3.     Two-tailed test: [ __ ]  Critical value tα/2 = ± __2.145____        α/2 = 0.05/2 = 0.025, when t.975 and v=14,  tα/2 = ±2.145  Use the t-distribution table to determine the critical value of tα or tα/2 Compare the values of test statistics, t, and critical value(s), tα or ± tα/2  ± tα/2 = ±2.145    tα = ±9.0795 Since tα lies in the rejection region, the null hypothesis Ho is rejected. This means that the projectile weight does affect the flying distance of the projectile.    Therefore Ho is __rejected_________.
Conclusion that answer the initial question	Ho is rejected, which means H1 is accepted. This means that the projectile weight does have an significant effect on the flying distance of the projectile.
Compare your conclusion with the conclusion from the other team members.	Comparing my results with Justin (Thor), who is using Runs #2 and #4.  Our results are the same, where the critical value lies in the rejection region. Hence, the null hypothesis (Ho) is rejected.
What inferences can you make from these comparisons?	I can infer that the projectile weight has an significant effect on the flying distance. (H1 is accepted) For Runs #1 and #3, the arm length is negative while the stop angle is negative. For Runs #2 and #4, the arm length is positive, while the stop angle is negative. This shows that a change in arm length also affects the flying distance, as our test statistic values are different (9.0795 and 4.471).
Your learning reflection on this Hypothesis testing activity	When I first learned Hypothesis testing, I was very confused😫because so much statistics were involved. I found it hard to identify the different abbrievations within the practice problems we did in class, and this led me to become very frustrated😠. Additionally, it took me very long to grasp a bit of what was covered in the youtube video. Since my brain cannot comprehend numbers very well, this topic was very challenging for me😰 Fortunately, I was able to understand how to carry out the calculations after listening to my friends' explanations as well as looking at their own calculations. I find it easier to grasp concepts when they are explained to me, so this method was helpful for me.  From this tutorial lesson and practices, I was able to learn how to analyse the results from the experiment and know whether to accept or reject my hypothesis. This can be done by using the two-tailed test. This knowledge will be very useful for me as I am currently carrying out an experiment in my elective module, Positive Psychology. In my experiment, I am determining whether the use of Gratitude will affect the mental well-being of working adults. In this case, the null hypothesis (Ho) is that Gratitude does not have any significant effect on the mental well-being of working adults, whereas the alternative hypothesis (H1) is that Gratitude does have a significant effect on the mental well-being of working adults.  Since I am going to collect results from surveys I have created, I can use this method of hypothesis testing to analyse the results obtained to prove if the null hypothesis (Ho) is accepted or rejected.  Furthermore, I can make use of hypothesis testing in my final year project as it will involve carrying out many experiments and obtaining a wide range of data and results. I may even make use of this during my internship as I will be doing work related to research!😎 As a result, I have come to appreciate using hypothesis testing to analyse data, even though I am not proficient in it😖Even when doing hypothesis testing for the DOE practical, I had to refer to the slides and workings for the practice questions multiple times to refresh my memory and see how to apply it in this exercise. I hope to practice more of this as I am carrying out my experiment for my elective module😁Over time, I hope to become better at it and to be able to use it in different areas whilst furthering my studies😊