Hypothesis Testing

 Hypothesis Testing

Based on our data collected from the DOE practical in which we manipulate 3 factors to determine which factor significantly affects the shooting distance. We will be using data from both Full Factorial and Fractional Factorial.

List of Team Members:

DOE PRACTICAL TEAM MEMBERS (fill this according to your DOE practical):

1. Cheong Jun Weng 

2. Roy Le Jing Hao

3. Beh Pei Jie 

4. Cao Yongjie

5. Adam Bin Sulaiman

Data collected for FULL factorial design using CATAPULT A 

 

Data collected for FRACTIONAL factorial design using CATAPULT B 

Jun Weng will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

Roy will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

Adam will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

Yongjie will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

Pei Jie will use Run #3 from FRACTIONAL factorial and Run#3 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):  Catapult A and Catapult B fires projectile at a similar distance. uA = uB u = distance between the landing point of projectile and catapult State the alternative hypothesis (H1): Catapult A and Catapult B fires the projectile  at a different distance uA ≠ uB u = distance between the landing point of projectile and catapult
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 A = 91.8 cm standard deviation A = 3.28 cm State the mean and standard deviation of sample catapult B: mean B = 90.3 cm standard deviation B = 2.84 cm Compute the value of the test statistic (t): v = 8 + 8 - 2 = 14
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 (0.975) = ± 2.145 Since t = 0.86 and t(0.975) = ± 2.145. Thus, - t(0.975) < t < + t(0.975) Since t = 0.86 falls within the accepted region, hence the null hypothesis is not rejected   Therefore Ho is not rejected
Conclusion that answer the initial question	Based on the results, the hypothesis that catapult A and B launches the projectile at a similar distance under similar factors is true. Thus, there is not performance difference between catapult A and B.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	I have observed that my teammates agree on the null hypothesis being acceptable. However, many did not show their working or methods thus I am quite confused as to who to verify my conclusion with. Thus, I decided to compare my conclusion with some of my class mates. They all have mixed results and conclusions. Some reject while some accepts the null hypothesis. The inference I could make is that comparing conclusions with teammates added with the entire class will be more accurate.  As comparing with a small group of people with similar conclusion made from carrying out a similar experiment in the same team may lead to bias. Thus, my ultimate inference is that the more data we have and share, the better our conclusions will be.