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Hypothesis Testing

 DOE Team member:

  • Rong Yiren
  • Tanapattanalux Kittitat
  • Xavier Chua
  • Benjamin Ang

FULL factorial data table

Factor A= Arm length
Factor B= Start angle
Factor C= Stop angle 
Result = Projectile flying distance

Run#Run OrderABCR1R2R3R4R5R6R7R8Ave.Std.Dev.
1 1---207.0208.3209.2204.0205.7209.4209.2208.3207.6 1.94 
2 3+--147.0158.0155.5160.0156.4158.1156.3155.1155.8 3.90 
3 2-+-161.5163.5156.4160.3160.4160.3164.0159.2160.7 2.41 
4 6++-111.5124.0123.7123.0125.0116.5121.0124.0121.1 4.72 
5 4--+113.5115.3106.0113.7100.5112.3110.5113.2110.6 4.97 
6 5+-+105.5109.5104.5103.0106.5107.0107.5105.0106.1 2.01 
7 8-++112.5114.0103.0108.0103.0105.0114.0113.0109.1 4.89 
8 7+++99.5102.5103.0105.0105.597.0105.599.0102.1 3.27 

Fractional factorial data table

Run#Run OrderABCR1R2R3R4R5R6R7R8Ave.Std.Dev.
2 3+--141.5146.5137.0146.0142.0142.0141.0149.5143.2 3.92 
3 2-+-153.5154.0164.0155.0161.0160.0158.0159.5158.1 3.71 
5 4--+105.0107.0107.0108.5104.5109.0110.5105.0107.1 2.16 
8 7+++108.5107.5104.5105.5106.5106.5107.5105.5106.5 1.31 

Scope of the test

Xavier Chua will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

Benjamin Ang will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

Tanapattanalux Kittitat will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

I (Yiren) will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.


Steps of hypothesis testing

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 = 36 cm

Start angle = 30 degree

Stop angle = 90 degree

 

Step 1:

State the statistical Hypotheses:

State the null hypothesis (H0):

CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

                              µ0 = µ1

 

 

State the alternative hypothesis (H1):

CATAPULT A produces the different flying distance of projectile as that of CATAPULT B.

                               µ0 ≠ µ1


 

 

 

 

 

Step 2:

Formulate an analysis plan.

Sample size is 2 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 = 102.1 m

 Standard deviation = 3.27

 

State the mean and standard deviation of sample catapult B:

 Mean = 106.5 m

 Standard deviation = 1.31


Compute the value of the test statistic (t):

Step 4:

Make a decision based on result

Two-tailed test:Critical value tα/2 = ± 2.145

        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 rejected.

 

 

Conclusion that answer the initial question

Since the test statistic t = 3.30 lies in the rejection region. The H0 is rejected. At 0.05 level of significance. Flying distance for catapult A produces a different flying distance of projectile as that of catapult B.

 

Compare your conclusion with the conclusion from the other team members.

 

What inferences can you make from these comparisons?

The conclusion from other team member are different from what I get, their conclusion said that the catapult A and catapult B produces a same flying distance of projectile as that of catapult B.

From these comparison with other member, It may because the data collected from run 8 is not very accurate. This can be due to many reason such as human error and enrioment factor. what can be improve to obtain a more accurate result is increase the number of data we collected. 


Reflection

Before this week's tutorial lesson.Hypothesis testing is a new knowledge for me. I thought it will be very complicate to master with this skill. Expecially when I saw the equations in the slides, they look very troublesome. However, after the tutorial lesson, my understanding on hypothesis testing get a great improvement. I am able to know the logic of the hypothesis and the meaning of each chataractors represent in the equation. After I did the practice questions to apply what I learn in tutorial. I believe that I can use hypothesis testing smoothly. I will practice this skill more in our future project.👍



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