Hypothesis Testing

 For the Hypothesis Testing blog entry, I was tasked to perform hypothesis testing on the data from the Design of Experiment practical regarding catapults. Below shows the results, conclusion and reflection of this entire assignment.

DOE PRACTICAL TEAM MEMBERS:

1. Bjorn Lim (Iron Man)

2. Darren (Hawkeye)

3. Gwyn (Captain America)

4. Cui Han (Black Widow)

5. Hai Jie (Hulk)

 Data collected for FULL factorial design using CATAPULT A:

Data collected for FRACTIONAL factorial design using CATAPULT B:

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: Run chosen: 7 Arm length = 24.5 cm Start angle = 25 degree Stop angle = 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): µ1 = µ2 Catapult A produces the same flying distance of projectile as that of catapult B.  State the alternative hypothesis (H1): µ1 =/= µ2 The  flying distance of the projectile is different for catapult A and catapult B.
Step 2: Formulate an analysis plan.	Sample size is 16. Therefore t-test will be used. Since the sign of H1 is =/=, a left/two/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 sample catapult A: n1 = 8 x̄1 = 96.2cm s1 = 3.44 cm State the mean and standard deviation of sample catapult B: n2 = 8 x̄2 = 91.3 cm s2 = 1.77 cm  Compute the value of the test statistic (t): v = 16 - 2 = 14 σ calculated= 2.924cm t calculated = 3.351
Step 4: Make a decision based on result	Type of test (check one only) Left-tailed test: [ __ ]  Critical value tα = - ______ Right-tailed test: [ __ ]  Critical value tα =  ______ Two-tailed test: [ /]  Critical value 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 Therefore Ho is rejected.
Conclusion that answer the initial question	Since the null hypothesis is rejected, the alternative hypothesis is accepted and hence the flying distance of the projectile is different for catapult A and catapult B.
Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?	Comparing the other team member’s results and conclusion, our results and conclusion are similar, all our t values lies in the rejection zone of the two-tailed test, meaning that the alternative hypothesis is accepted instead of the null hypothesis. From comparing the other team member's results and conclusion, this increases the reliability of my comparison between catapult A and B, and hence I can comfortably conclude that overall the flying distance distance of the projectile is different for catapult A and catapult B when comparing ALL 4 runs, when different settings like the arm length, start angle and stop angle are tweaked and adjusted.

Reflection

From this mini assignment, since I had performed hypothesis testing before, from the practice questions given during lesson, this blog entry serves as a refresher and practice in performing this skill. However with that being said, this assignment is different from the practice questions because I am performing hypothesis testing using real data I have recorded from a previous practical, therefore giving me experience in applying this skill to real world situations (if that makes sense). This skill will help me in upcoming projects, which includes designing an object in the Project Development lesson soon, and the capstone project in a few months time. 

Overall, I find that hypothesis testing include lots of mathematical formulas needed to calculate the values required, and being a math kind of person, this lesson has been really enjoyable for me. Furthermore, it provided me with a way to calculate the validity of both hypotheses in a mathematical way rather than gauging and "eyeballing" the values and recklessly coming up with a conclusion based on that.