Hypothesis testing

Hello! Welcome back to my blog. This week I am tasked to do hypothesis testing based on my Design of experiment catapult practical. Here is a summary of the steps I will be doing to justify my hypothesis. I am person C (Captain America), so I will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

The QUESTION	The catapult (the ones that were used in the DOE practical) manufacturer needs to determine the consistency of the products they have manufactured. Therefore they want to determine whether CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.
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 and catapult B is collected using the factors below: Arm length =  _28___cm Start angle = __0___ degree Stop angle = __90___ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The flying distance the projectile was launched by catapult A and B is the same. State the alternative hypothesis (H1): The flying distance the projectile was launched by catapult A and B is different.
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 sample catapult A: Mean: 90.5 cm Standard deviation: 5.32 cm State the mean and standard deviation of sample catapult B: Mean: 101.5 cm Standard deviation: 3.48 cm   Compute the value of the test statistic (t):   n1 = 8 n2 = 8 V = 8 + 8 – 2    = 14 x̄1 = 101.5 cm x̄2 = 90.5 cm s1 = 3.48 cm s2 = 5.32 cm    σ = 4.806  t = 4.577
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 = ± ___t0.975___                                                                                           = 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 Therefore Ho is ___rejected____.
Conclusion that answer the initial question	Since t = 4.577 lies in the rejection region, the null hypothesis is rejected. Hence, the alternative hypothesis (H1): “The flying distance the projectile was launched by catapult A and B is different” is correct. At 0.05 level of significance, the catapults produced by the manufacturer are not consistent.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Looking at everyone’s conclusion, the majority of the results support the alternative hypothesis because the critical values lie in the rejection zone of the test statistic value. Hence, the general conclusion is that the flying distance the projectile was launched by the catapult is different.  I can infer that my conclusion is more reliable and valid as the majority of my team members also ended with the same conclusion. Hence, the flying distance produced by the 2 catapults will always be different for different types of settings

Reflection

In this topic, I am supposed to form a hypothesis based on the situation given to me and prove whether it is valid or not. Previously during the tutorial session, I had already done some practice questions given to me as a warm-up and had understood the procedures to test the validity of my hypothesis. So this exercise is like a refresher to me and it requires me to find out whether the catapults the manufacturer produced have consistent flying distance when put under the same conditions. I think this topic is important because it helps us to identify the margin of error and adjust to it accordingly. It is also very applicable in the working world in order to produce the best quality products. What made this topic interesting is that it is heavy on mathematics and calculation is something I enjoy doing, so this topic sparked my interest. This topic can be useful for the project in CP5070 as it helps me to minimize the degree of error in my product so that I can produce an ideal product that is very close to my plan. I used to think that hypothesis testing can just be concluded from the practical itself and does not require much calculations. However, now I realized that every product cannot be 100% perfect and an acceptable and rejected range must be identified so that every function of every of the same product produced does not stray so far from one another. Next, I will continue to do more practice and work on my calculation skills by going onto YouTube to find examples.