Hypothesis Testing

For this week of blogging, I will be writing about the experience that I obtained from hypothesis testing using full and fractional. The 3 factors used are the Length of the Catapult Arm(A), Start angle(B), Stop angle(C).

Below show the data obtained for Full Factorial: 

The data below show what was obtained for Fractional design:

Brayden will use Run 5 from Fractional Factorial and Run 5 from Full Factorial.

Jolyn will use Run 3 from Fractional Factorial and Run 3 from Full Factorial.

Kalyani will use Run 4 from Fractional Factorial and Run 4 from Full Factorial.

Gideon will use Run 6 from Fractional Factorial and Run 6 from Full Factorial.

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 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 =  24.1cm Start angle = 0 degree Stop angle = 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): U1 = U2 There will not be any effect on the distance the projectile can fly State the alternative hypothesis (H1): U1 ≠ U2 There will be an effect on the distance that the projectile can fly
Step 2: Formulate an analysis plan.	The sample size is 8 < 30. Therefore t-test will be used. Since the sign of H1 is ≠, a two-tailed test is used. The 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: 105.6 Standard deviation: 1.78  State the mean and standard deviation of sample catapult B: Mean: 117.0 Standard deviation: 3.07 Compute the value of the test statistic (t):
Step 4: Make a decision based on the result type	Type of test  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 T = -8.50 Therefore Ho is rejected.
The conclusion that answers the initial question	To conclude, there is an effect on the distance traveled by the projectile based on the calculation made above.
Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?	By comparison between my conclusion with Kalyani and Jolyn’s conclusion. It is safe to say that H。is rejected hence, the different users have an effect on the flying distance of the projectile.  Out of the many inferences, I will write 2 which I found to be the most interesting. The first inference would be that the different rubber bands have different strengths in tension. Some rubber bands are tighter hence increasing the strength of the catapult while other rubber bands are looser so it has caused the catapult to have less strength. It is difficult to find rubber bands of equal tightness. Another inference was the start angle for the 2 catapults is different. For catapult A, the original start angle is not truly 0० as it is slightly more tilted while catapult B has a normal 0०. Thus, the distance recorded could be affected by these 2 inferences

Reflection:

After learning about hypothesis testing, I realised that it was a concept that is pretty easy to learn but not master. Hence, I knew that I will be revisiting the lesson material when I need. After, the practical and the lesson practice, I can use hypothesis testing for any project that requires this skill

Design of Experiment(DOE)

For this week, I was assigned case 1 for the Design of Experiment. Hence I used Excel to find out how many uncooked kernels are left in the bag. I assign 3 factors according to A being Diameter, B for Microwaving time, and C for Power. 

The table below shows the data provided.

So, to compare the factors in 1 graph, I will need to find the average of High/Low A, B, and C. Thus, the graph below will show the Full Factorial Analysis.

As shown above, the gradient from each line shows how much change. Hence it can be determined that C(Power) has the biggest change in gradient while A(Diameter) has the least change for the gradient.

The tables and graphs below will show the interaction effect between 2 factors. The interaction effect is basically what 1 factor does to the other factor when there are different values. Hence I have done the interaction effect of (AxB),(AxC),(BxC).

In AxB, the gradient for High B is negative while Low B is positive. Hence there is significant interaction between A and B

In AxC, the gradient change is not that huge so there is not a big significant interaction between A and C.

In BxC, both gradients are negative and for one there is a steep gradient. So, there is a big significant interaction between B and C.

For Fractional Factorial Design, I choose the results from runs 2,3,5,8 as there are factors of both - & + equal number of times. This will result in an orthogonal design with good statistical properties

As shown in the graph above.

A(Diameter of the bowl) increased from 10 to 15cm, the mass of the bullets increase from 1.15g to 1.9g.

B(Microwaving time) increases from 4 to 6 minutes, the mass of bullets decreases from 2.1g to 0.95g.

C(Power) increases from 75% to 100%, the mass of bullets decreases from 2.55g to 0.50g.

So, what can be seen from the graph would be that the gradient for Power is the steepest followed by Microwaving time and lastly Diameter. There are similarities between Fraction Factional and Full Factorial so using Fraction Factional is more desirable as fewer runs are done hence, less time and materials are needed to get the same results

When converting Excel to Google Sheets, the file was corrupted so I was only left with the screenshots I took.