Hypothesis Testing 

For this assignment, you will use the DOE experimental data that your practical team have collected both for FULL Factorial and FRACTIONAL Factorial.

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

1. Serena (Iron man)

2. Trisyia (Thor)

3. Jun Xiang (Captain America)

4. Kai Rong (Black Widow)

5. Person E (Hulk)

6. Jerome (Hawkeye)

 

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result)

 

Data collected for FRACTIONAL factorial design using CATAPULT B (fill this according to your DOE practical result):

 

Iron Man will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

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

Captain America will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

Black Widow will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

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

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

 

USE THIS TEMPLATE TABLE and fill all the blanks

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 =  32.6cm Start angle = 20 degree Stop angle = 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): At arm length of 32.6cm, start angle of 20 degree and stop angle of 90 degree, using a different catapult will not affect the flying distance. X = µ     State the alternative hypothesis (H1): At arm length of 32.6cm, start angle of 20 degree and stop angle of 90 degree, using a different catapult will affect the flying distance X > µ
Step 2: Formulate an analysis plan.	Sample size is 8 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 sample catapult A: Mean = 83.5 Standard deviation = 3.15   State the mean and standard deviation of sample catapult B: Mean = 80.9 Standard deviation = 3.31     Compute the value of the test statistic (t): n1 = 8 n2 = 8 s1 = 3.15 s2 = 3.31 X1 = 83.5 X2 = 80.9
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: [ 1.51 ]  Critical value tα =  1.860 3.    Two-tailed test: [ __ ]  Critical value tα/2 = ± ______   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 accepted.
Conclusion that answer the initial question	At arm length of 32.6cm, start angle of 20 degree and stop angle of 90 degree, using a different catapult will not affect the flying distance.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Both Kai Rong and my decision was the same in that the flying distance between both catapults were the same. While the rest had the conclusion that the flying distance of both catapults were different.   The inference made is that the catapults made are inconsistent because although me and Kai Rong obtain the result of  same flying distance, majority of the results were deemed to be different flying distance meaning the catapults were inconsistent to each other.

Reflection

For this lesson I learnt how hypothesis testing is useful in making sure products manufactured provide consistent results when the same two items is used example being the catapults which both are exactly the same product but produce different flying distance. This shows the products' inconsistency and can allow the manufacturer to research more and learn how to improve the products' consistency. I used to think that hypothesis testing is just testing of the results and comparing data and is kind of pointless to do. Now I think that it is important to do in order to improve a products overall quality. So next, I will try to implement it onto our prototype if possible.