Hypothesis Testing

 

HYPOTHESIS TESTING TASK FOR INDIVIDUAL BLOG

 

For this assignment, you will use the DOE experimental data that your practical team have collected both for FULL Factorial and FRACTIONAL Factorial.

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

1. Bjorn Lim (Iron Man): Run 1

 

2. Darren (Hawkeye): Run 7

 

3. Gwyn (Captain America): Run 6

 

4. Cui Han (Black Widow): Run 4

 

5. Hai Jie (Hulk)

 

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):

 

I will be doing calculations for Run 6:

Full Factorial (Catapult A)

Run#	Run Order	A	B	C	D=AB	E=AC	F=BC	G=ABC	R1	R2	R3	R4	R5	R6	R7	R8	Ave.	Std.Dev.
6	5	+	-	+	-	+	-	-	102.0	103.5	108.0	106.5	96.5	103.5	96.5	105.0	102.7	4.25

Fractional Factorial (Catapult B)

Run#	Run Order	A	B	C	D=AB	E=AC	F=BC	G=ABC	R1	R2	R3	R4	R5	R6	R7	R8	Ave.	Std.Dev.
6	5	+	-	+	-	+	-	-	92.5	95.2	98.7	95.9	98	93	94.9	94	95.3	2.21

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 =  27.5cm Start angle = 10 degrees 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. H0 : µ1 = µ2 State the alternative hypothesis (H1): CATAPULT A produces the a different flying distance of projectile than that of CATAPULT B. H1 : µ1 ≠ µ2
Step 2: Formulate an analysis plan.	Sample size is 8 (<30) 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: Average = 102.7 cm Standard Deviation = 4.25 cm State the mean and standard deviation of sample catapult B: Average = 95.3 cm Standard Deviation = 2.21 cm Compute the value of the test statistic (t): σ = 3.621 v = 14 t = 4.087
Step 4: Make a decision based on result	Type of test (check one only) Left-tailed test: [ __ ]  Critical value tα = - ______ Right-tailed test: [ __ ]  Critical value tα =  ______ Two-tailed test: [✔ ]  Critical value tα/2 = ± ±2.145 Use the t-distribution table to determine the critical value of tα or tα/2 α/2 = 0.05/2 = 0.025 v = 14 From appendix 1, at t = 97.5  tα/2 = ± ±2.145 t = 4.087 Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 t >  tα/2  Therefore Ho is not accepted.
Conclusion that answer the initial question	At 0.05 level of significance, both catapults produce the different flying distance of projectile. Hence CATAPULT A produces the a different flying distance of projectile than that of CATAPULT B.
Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?	My conclusion is similar to that of my team members.  For example, Darren’s values of test statistics, t=3.351 which is also too large to be accepted. Therefore it does not fall into the acceptable range and the null hypothesis is not accepted. This shows that no matter which run is used, a good sample size will show the same correlation.

For this task, communication is very important, especially wherein my groupmates are not the same people who I usually work with in this module. Having done the exercises before also helped. When doing the exercises, I had to communicate with my group as well as refer to my calculations in the past to make sure that I recall and apply everything that I learnt.