Hypothesis Testing

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

DOE Practical Team Members:

1. Heng Leon
2. Rufus How
   
3. Sean Tay
4. Ethan Chan
5. Alton Yau

Data collected for FULL factorial design using Catapult A

Data collected for FRACTIONAL factorial design using Catapult B

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:

The human factor is assumed to be negligible. Therefore the different users will not have any effect on the flying distance of the projectile.

Flying distance for catapult A and catapult B is collected using the factors below:

Arm length =  _ cm

Start angle = _ degree

Stop angle = _ degree

H₀: Catapult A has the same flying distance of projectile as that of Catapult B.  μ1=μ2

H₁: Catapult A does not have the same flying distance of projectile as that of Catapult B. μ1≠μ2

The sample size is 16, 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 5%.

Using run #8 from FRACTIONAL factorial and run #8 from FULL factorial.

Catapult A:

Mean = 91.9

Standard Deviation = 2.90

Catapult B:

Mean = 91.9

Standard Deviation = 2.90

Testing Difference of means:

Test Statistics (t) 

t = 0

v = 8 + 8 - 2

v = 14

At significance level of 5%, 

Area = 1 - (0.05/2)

Area = 0.975

From Student's t Distribution Table, 

At t,0.975 and v = 14

t = ±2.145

Since the t-test value falls within the acceptance region hence Ho is accepted.

Therefore at the significance level of 5% Catapult A has the same flying distance of projectile as that of Catapult B.

After comparing the conclusion from the other team members, it is also seen that both Catapult has the same flying distance regardless of the significance level. Thus, it can be said that the manufacturer is consistent in the quality of catapults that are being produced.

Reflection

After going through the activity, it was a good refresher of how the hypothesis testing is being done and how the 5 steps are very systematic. It is also important to craft out the hypothesis statement which answers what the scenario wishes to address. 

Making sense of the result after calculation and making a decision whether to accept the null or alternative hypothesis is important as this would be the crucial step in crafting your conclusion which is ultimately related to your null and alternate hypothesis.

Overall, hypothesis testing would require more contextualizing of data than just blindly following the different steps which might lead to another conclusion that does not fit your calculated results.