Hypothesis Testing

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

DOE PRACTICAL TEAM MEMBERS:

1. Gideon (Me)

2. Brayden

3. Kalyani

4. Jolyn

 

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 use Run #6 from FRACTIONAL factorial and Run#6 from FULL factorial.

Brayden will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

Kalyani will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.

Jolyn will use Run #3 from FRACTIONAL factorial and Run#3 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 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 =  30.5 cm Start angle = 0 degree Stop angle = 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0):  μA = μB The flying distance of the projectile from Catapult A will be the same as the flying distance of the projectile from Catapult B.   State the alternative hypothesis (H1): μA ≠ μB The flying distance of the projectile from Catapult A will not be the same as the flying distance of the projectile from 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.
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A:  Mean: 108.1 cm Standard Deviation: 9.04 cm   State the mean and standard deviation of sample catapult B:  Mean: 112.9 cm Standard Deviation: 7.24 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  Since t = - 1.907, Therefore Ho is accepted.
Conclusion that answer the initial question	Since the null hypothesis is accepted, the flying distance of the projectile from Catapult A will be the same as the flying distance of the projectile from Catapult B.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	While my null hypothesis is accepted, my other team members have their null hypothesis rejected. Comparing with my other classmates, their null hypothesis have also been rejected. only very few of my classmates have their null hypothesis is accepted. I can infer that my run is an outlier, since most of my classmates have a rejected null hypothesis.

 

Reflection

When I first learnt about hypothesis testing, I was overwhelmed by the techniques that were used to obtain whether the null hypothesis is accepted or rejected. I was not sure on how to craft the null and alternative hypothesis, but with practice and this task as a refresher, I got it down. This skill will help me in future projects and experiments.