Hypothesis Testing

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For this assignment, I will be using the DOE experimental data that my practical team has collected for both for FULL factorial and FRACTIONAL factorial.

My team members consist of:

  1. Lionel
  2. Anthony 
  3. Firman
  4. Wei Xue


Full Factorial





Fractional Factorial




Question:

The catapult 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.





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

 


Scope of the Test:

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

Arm length = cm

Start angle = degrees

Stop angle = LOW


Stating the statistical Hypothesis:


State the null hypothesis (H0):

Flying distance of projectile launched Catapult A is the same as from catapult B

Ho : µ1=µ2

 

State the alternative hypothesis (H1):

Flying distance of projectile launched Catapult A is the different from catapult B

H1 : µ1 ≠ µ2



Formulating the analysis plan:

Sample size is 16,Therefore t-test will be used.

Since the sign of H1 ≠ ,a two tailed test is used.

Significance level (α) used in this test is 5%



Using Run #3 from Full and Fractional Factorial:

Catapult A: Mean = 90.3 , Standard Deviation = 2.28 

Catapult B: Mean = 91.3, Standard Deviation = 3.30


v  =  8 + 8 - 2  = 14

t = -0.66

At significance lvl of 5%,

Area = 0.95 + 0.05/2 = 0.975


From the Distribution Table,

@ v =14 and t0.975 :

t = 2.145

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



Conclusion:

At a significance level of 5%, Ho has fallen into the acceptance range and hence been accepted, which shows that Catapults A and B produced the same flying distance of projectile.

By comparing conclusions with my other team members, I found that similarly, all of their t-test values had fell into their acceptance ranges, which lead to them accepting their null hypotheses(Ho). 



Reflection:

After this activity on Hypothesis testing, it has helped me understand and put into practice practice the ways of different testing methods and data collection for such methods. However, I find myself confused with the values of t and the plotted graphs for finding the acceptance ranges, which is something that I will have to look out for and improve on. 



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