Hypothesis Testing Blog Entry

 

Data collected for FULL factorial design using CATAPULT A 

Person B: (Thor)

Thor will use will use Run #2 and Run#4. To determine the effect of projectile weight.

Factor A: Arm Length 

Factor B: Projectile Weight 

Factor C: Stop Angle 

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 is collected using the factors below: Arm length =  33 cm Projectile weight = 0.86 grams and 2.0 grams Stop angle = 90 degrees
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Using the lighter projectile weight from Run #2 and the heavier projectile weight from Run #4 would result in the same distance travelled by the projectile.  𝜇2 = 𝜇4 State the alternative hypothesis (H1): Using the lighter projectile weight from Run #2 would result in a further distance travelled than the heavier projectile weight from Run #4.                                             𝜇2 > 𝜇4
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 : 175.0 cm Standard Deviation: 3.32 cm   State the mean and standard deviation of Run #4:  Mean : 152.3 cm Standard Deviation: 3.39 cm   Compute the value of the test statistic (t):
Step 4: Make a decision  based on result	Type of test (check one only)              Right-tailed test: [✓]  Critical value tα =  1.761   Compare the values of test statistics, t, and critical value(s), tα    Therefore Ho is false.
Conclusion that answer the initial question	Using the lighter projectile weight would result in a further distance travelled than the heavier projectile weight.
Compare your conclusion with the conclusion from the other team members.	Yan Zhen (Captain America): Using a smaller stop angle would result in a larger flying distance of the projectile while using a bigger stop angle would result in a shorter flying distance.  Jeevan (Black Widow): Using a smaller stop angle would result in a larger flying distance of the projectile while using a bigger stop angle would result in a shorter flying distance.  Ngo Van Anh (Iron Man): Using a lighter projectile weight would result in a larger flying distance of the projectile while using a heavier projectile weight would result in a shorter flying distance.  Jeremy (Thor): Using a lighter projectile weight would result in a larger flying distance of the projectile while using a heavier projectile weight would result in a shorter flying distance.
What inferences can you make from these comparisons?	From these comparisons, I can infer that: using a lighter projectile weight would result in a larger flying distance for the projectile than using the heavier projectile weight. using a small stop angle would result in a further flying distance for the projectile than using a larger stop angle. Therefore, to achieve the maximum flying distance, we should use a smaller projectile with a smaller stop angle.
Your learning reflection on this Hypothesis testing activity	When we first started the Hypothesis testing activity, I found it quite tedious and I thought that it would not be very interesting. However, through doing this practical activity I found how practical the whole process could be, and how powerful it is in confirming theories and coming to conclusions about data in order to help with future activities. To start, the hypothesis testing procedure starts with coming up with a null hypothesis and an alternative hypothesis for the experiment. After this, we have to decide whether to make use of a one-tailed or two-tailed test, before then carrying out the test to find out the validity of the initial hypothesis. To prepare us for this activity, our teacher introduced us to the concepts of the hypothesis testing procedure to familiarise us to the process. Our teacher also allowed us to apply what we learnt from the concepts into some practice questions. Overall, from this experience, I realised how powerful the whole process can be if it is applied well, and I will be looking forward to making use of it in my future projects!