Hypothesis Testing

HYPOTHESIS TESTING TASK FOR INDIVIDUAL BLOG 

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 Jun Weng (Iron Man) 

2. Roy (Thor) 

3. Adam (Captain America) 

4. Yong Jie (Black Widow) 

5. Pei Jie (Hulk) 

6. Person F (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 = 34 cm  Start angle = 0 degree  Stop angle = 60 degree
Step 1:  State the   statistical   Hypotheses:	State the null hypothesis (H0):  μ1 = μ2, Flying Distance of both catapults are the same  State the alternative hypothesis (H1): μ1 ≠ μ2 , Flying Distance of both catapults are different
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: x̄1 = 153.4 S1 = 3.10  State the mean and standard deviation of sample catapult B: x̄2= 150.2  S2 = 5.61  Compute the value of the test statistic (t):  σ = sqareroot(8(3.10)2 + 8(5.61)2  / 8 + 8 − 2) σ = 4.85  t =  153.4−150.2/4.85squareroot(⅛+⅛) t = ±1.321
Step 4:  Make a decision  based on result	Type of test (check one only)  1. Two-tailed test: [±1.321]  α = 0.05  percentile = 1-0.05/2 = 0.975  Critical value t0.975 = ± 2.145  Use the t-distribution table to determine the critical value of tα or tα/2

	Two-tailed test  Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 Since t falls in the acceptance region,   Therefore Ho is accepted.
Conclusion that  answer the initial  question	Catapults A and B allow similar flying distances for the projectiles
Compare your   conclusion with  the conclusion  from the other  team members.  What inferences  can you make   from these   comparisons?	Most of my teammate’s conclusion were similar to mine as Ho is accepted due to  the catapults only having an insignificant difference.

Reflection: 

This practical requires us to use the data collected from the DOE practical on the flying distance  allowed by a catapult to then perform hypothesis testing. Since 2 different catapults were used, 1  run from each catapult with the same factors were selected as the sample means. Since the  hypothesis was given, the task was to prove whether the hypothesis was null or valid. Hypothesis  testing in this case, is important as it helps determine if both catapults allowed the same projectile  distance and also whether the catapults can be used interchangeably or which catapult allowed the  longest distance. This was interesting for me as I got to perform hypothesis testing with data that I 

collected and understood instead of sample data, which made it clearer. Hypothesis testing can also  be used for our project when trying to determine whether our hypothesis is valid.  

I used to think that the hypothesis can just be determined by comparing the data collected but now I  know that just because the data collected was slightly different from each other doesn’t mean that  hypothesis is not null. The next time I have to use hypothesis testing would probably be for the  capstone project. This time I will put this knowledge to good use when conducting experiments.