Hypothesis Testing

 Hypothesis Testing                                                                                                          27 January 2022

DOE PRACTICAL TEAM MEMBERS (fill this according to your DOE practical):

1. Serena (Iron Man)

2. Trisyia (Thor)

3. Jun Xiang (Captain America)

4. Kai Rong (Black Widow)

5. Person E (Hulk)

6. Jerome (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 = 32.6 cm Start angle = 20 degree Stop angle = 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Ho=H1 At the same factor level of 32.6 cm Arm length, 20 degree Start angle and 90 degree Stop angle, Catapult A produces the same flying distance of projectile as that of Catapult B.     State the alternative hypothesis (H1): Ho ≠ H1 At the same factor level of 32.6 cm Arm length, 20 degree Start angle and 90 degree Stop angle, Catapult A produces a different flying distance of projectile as that of Catapult B.
Step 2: Formulate an analysis plan.	Sample size is _8_ Therefore t-test will be used.     Since the sign of H1 is _≠__, a left/two/right tailed test is used.     Significance level (α) used in this test is _0.05 or 5%_
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: X̄A = 83.5 cm ; s1 = 3.15 cm     State the mean and standard deviation of sample catapult B: X̄B = 80.9 cm ; s2 = 3.31 cm     Compute the value of the test statistic (t):
Step 4: Make a decision based on result	Type of test (check one only) 1.     Left-tailed test: [ __ ]  Critical value tα = - ______ 2.     Right-tailed test: [ __ ]  Critical value tα =  ______ 3.     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 is _not rejected(accepted)_____.
Conclusion that answer the initial question	Since the test statistic, t=1.501 lies in the acceptance region, the null hypothesis is not rejected (accepted). At 0.05 significance, same factor level of 32.6 cm Arm length, 20 degree Start angle and 90 degree Stop angle, Catapult A produces the same flying distance of projectile as that of Catapult B. This means that the manufacturer’s products are consistent.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Person A (Serena): Catapult A and B produces different projectile flying distance. Person B (Trisyia): Catapult A and B produces different projectile flying distance. Person C (Jun Xiang): Catapult A and B produces different projectile flying distance. Person D (Me): Catapult A and B produces same projectile flying distance. Person F (Jerome): Catapult A and B produces same projectile flying distance.   Majority (3 out of 5) concluded that Catapult A and B produces different projectile flying distance while minority (2 out of 5) concluded that Catapult A and B produces same projectile flying distance. However, for the 2 minority Person D and F, the run chosen is the same. Hence, it can be taken that 75% of the team concluded that Catapult A and B produces different flying distance. Therefore it can be concluded that the manufacturer’s products are inconsistent.

Reflection

In this blog assignment, we were tasked to apply and perform hypothesis testing learnt from the tutorial session onto the practical that we had conducted on catapult projectile flying distance. From the data collected on the projectile flying distance, we were supposed to compare between full factorial and fractional factorial using the same run to find out whether the catapult used in the full factorial under the same setting produces the same or different projectile flying distance as the catapult used in the fractional factorial. For this practical, we were split into different groups so it was a good experience to learn how to work and communicate with different people as in the future or work force, we would not always be able to work with the same team or people that we like. Learning how to work with different people is an important skill set not only in school but in workforce as we would be able to adapt and be comfortable working with other people. 

The assignment required us to apply the hypothesis testing framework/concept and using our data from the experiment to find out whether the catapults were consistent. It was a more engaging and interesting way to teach us to apply the concept as we had completed the practical ourselves, so we are more familiar and makes more sense to us compared to asking some tutorial questions. Learning how to perform hypothesis testing is important as it is a formal procedure used by researchers or experimenters to accept or reject statistical hypotheses. It teaches us a proper way to test a hypothesis instead of randomly doing it and would be helpful in our FYP or creating a prototype in CP5070 where we would be able to apply hypothesis testing to test different hypothesis to improve or make our product better. It can also go hand in hand with DOE which allows us to find out the effect of different factors on our product and overall improves or make our product more efficient.

I used to think that Hypothesis Testing and DOE would be very difficult as it would require a lot of analytical skill and use of excel to read the data. However, after going through the tutorial lesson with practice questions and this assignment, now i think that the concept of Hypothesis Testing is not that difficult to analyse as all i need to do is to follow the step-by-step framework then i would be able to complete the hypothesis testing. In addition, after Dr Noel retaught and clarified the concept on DOE, i can better understand and am able to even create a simple excel workbook myself for my DOE case study. So next i will be able to apply and use them in my internship or FYP to further improve my product.