Hypothesis Testing

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

1. Person A (Iron Man): Anwar

2. Person B (Thor): Katrina

3. Person C (Captain America)

4. Person D (Black Widow): Kieran

5. Person E (Hulk): Jun Lin

6. Person F (Hawkeye)

 

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result):

A: Run #3

A	B	C	R1	R2	R3	R4	R5	R6	R7	R8	Ave	Std. Dev
-	+	-	155.8	153.5	159.0	154.5	152.5	149.5	156.5	152.0	154.2	2.96

 

Data collected for FRACTIONAL factorial design using CATAPULT B (fill this according to your DOE practical result):

B: Run #3

A	B	C	R1	R2	R3	R4	R5	R6	R7	R8	Ave	Std. Dev
-	+	-	157.8	153.5	158.5	154.5	150.5	149.5	159.5	153.0	154.6	3.70

 

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.

 

A: Run #3

A	B	C	R1	R2	R3	R4	R5	R6	R7	R8	Ave	Std. Dev
-	+	-	155.8	153.5	159.0	154.5	152.5	149.5	156.5	152.0	154.2	2.96

B: Run #3

A	B	C	R1	R2	R3	R4	R5	R6	R7	R8	Ave	Std. Dev
-	+	-	157.8	153.5	158.5	154.5	150.5	149.5	159.5	153.0	154.6	3.70

 

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 =  34 cm Start angle = 30 ° Stop angle = 90 °
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Catapult A produce the same flying distance of projectile as that of Catapult B Null hypothesis, H0 : µ1 = µ2   State the alternative hypothesis (H1): Catapult A does not produces the same flying distance of projectile as that of Catapult B Alternative hypothesis, H1 : µ1 ≠ µ2
Step 2: Formulate an analysis plan.	Sample size is 8 replicates < 30. 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 as it is the default value and is less stringent due to its smaller acceptance region.
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: Mean = 154.2cm Standard deviation = 2.96   State the mean and standard deviation of sample catapult B: Mean = 154.6cm Standard deviation = 3.70   Compute the value of the test statistic (t): σ=      = 3.58 v = 8+8-2 = 14 t =    = -0.22346
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: [ü] 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   Since significance level will be distributed to two-tail, α/2 = 0.05/2 = 0.025 Percentile = 1-0.025 = 0.975 From Appendix 1, at v = 14, t0.975 = = ±2.145 The value of test statistic, t = -0.22346 > t0.975 = -2.145, hence t will lie in the acceptance region. Therefore, Ho is accepted.
Conclusion that answer the initial question	Since test statistic, t = -0.223 lies in acceptance region, null hypothesis is accepted. At 0.05 level of significance, both catapults produce the same flying distance of projectile. Hence, the products the catapult manufacturer has manufactured are consistent.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Kieran – same conclusion Junlin – same conclusion Anwar – same conclusion   As all the team members in the team got the same results of both catapults producing the same flying distance of projectile, the products the catapult manufacturer manufactured were thus consistent.   I can infer that at different arm length, start and stop angle, the catapults give consistent results of the same flying distance of projectile.

 

Reflection:

Hypothesis Testing helped me to understand how to we can compare a sample against a sample and a sample against a population to determine our hypothesis results. At first, I found this tutorial quite hard with all the mathematical calculations but after trying out the practice questions, I got the hang of determining the hypothesis claim as it follows a technical approach. A statistical hypothesis testing is an assumption about a population parameter which may or may not be true. It refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses. The ideal way to determine if a statistical hypothesis is true is by examining the entire population. However, in real life, that would deem to be impractical as the population size is huge and it would take lots of energy and time to examine the whole population. Thus, we would examine only the sample from the population size and if the sample data is not consistent with the statistical hypothesis, the hypothesis is rejected. The steps to follow in hypothesis testing is to first state the hypotheses (H₀ and H₁). The null (H₀) and alternative (H₁) hypothesis are mutually exclusive of each other. Followed by formulating an analysis plan (t test for n ≤30, z test for n ≥30 and signs to determine one/two tailed test). Next, we would use an appropriate formula (sample vs sample or sample vs population) to calculate the test statistic based on sample data and finally make a decision based on results by accepting or rejecting the null hypothesis using the curve on acceptance and rejection regions.

I had a great insight and meaningful takeaways from this tutorial with all of the new concepts and terms I have learnt to perform my next hypothesis testing. With this knowledge learnt, I am able to perform a hypothesis testing better for future projects. I learnt that hypothesis testing is important as we would need to evaluate the performance of our product by measuring its validity and reliability outcomes but taking results from the entire population is time-consuming and thus we would resort to taking a sample size from the population size and determine its consistency. With hypothesis testing, we could better understand what improved or went wrong with the systemic investigation and make changes to it to improve the user’s experience.