Hypothesis testing

 

My teammates are:

                                Miguel

                                Nigel   

                                Madelaine

                                Myself

This is the Full Factorial

                                        figure 1: full factorial graph

Here is Fractional Factorial

figure 2: fractional factorial data table

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 =  __31__cm Start angle = ___0__ degree Stop angle = __60___ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): U1:flying distance using catapult A U2:flying distance using catapult B U1=U2     State the alternative hypothesis (H1):    U1≠U2
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:143.5 standard deviation:6.52     State the mean and standard deviation of sample catapult B:  mean:154.9 standard deviation:1.15     Compute the value of the test statistic (t):
Step 4: Make a decision based on result	V=14,T0.975 Critical value tα/2 = ± __2.145____       Therefore Ho is _____rejected______.
Conclusion that answer the initial question	at 0.05 significance level, t=-4.56 lies within the rejected region, so H0 is rejected. so catapult A and catapult B do not produce the same flying distance.
Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?	the conclusion for all the team members except for Miguel is same which is that, Catapult A and B do not produce the same flying distance. I can infer that the catapults that is manufactured are mostly inconsistent.

I was first perplexed about how to do hypothesis testing, especially after going over the slides before to the session, and after looking at the various equations and graphs, I assumed it would be quite hard and time-consuming. However, as my lecturer went through the course and we practiced a few times, I realized that it was really manageable and quite beneficial, especially for my FYP.