Hypothesis Testing

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

DOE PRACTICAL TEAM MEMBERS 

1. Lionel Neo

2. Goh Wei Xue

3. Firmanshah

4. Anthony Lee

 

Data collected for FULL factorial design using CATAPULT A 

Data collected for FRACTIONAL factorial design using CATAPULT B 

 

Lionel will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

Wei Xue will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

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

Anthony will use Run #8 from FRACTIONAL factorial and Run#8 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 = 27.3 cm Start angle = 3 degree Stop angle =  LOW
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Catapult A produces the same flying distance of projectile as catapult B Ho : µ1=µ2     State the alternative hypothesis (H1): Catapult A does not produce the same flying distance of projectile as catapult B H1 : µ1 ≠ µ2
Step 2: Formulate an analysis plan.	Sample size is 16, therefore t-test will be used.     Since the sign of H1 ≠ ,a two tailed test is used.     Significance level (α) used in this test is 5%
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: Mean = 131cm Standard Deviation = 2.73     State the mean and standard deviation of sample catapult B: Mean = 129.9cm Standard Deviation = 1.59     Compute the value of the test statistic (t):   t = 0.921
Step 4: Make a decision based on result	Type of test        Two-tailed test:      v = 16-2 =14      α = 1 - (0.05/2)         = 0.975       Critical value tα/2 = ± 2.145   Use the t-distribution table to determine the critical value of tα or tα/2     At a significance level of 5% v = 14 t.975 = t = ±2.145   Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 t = 0.921 > tα/2 = ± 2.145 Therefore Ho is accepted.
Conclusion that answer the initial question	Since the test value falls within the range of tα/2 = ± 2.145, Ho is accepted and the hypothesis that catapult A has the same flying distance as catapult B is correct.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	After comparing conclusions, it is observed that all of my team members used different runs with different settings and still managed to get test values that fell within the range of the same significance levels, hence they all accepted their null hypotheses(Ho). I can infer from the conclusions of me and my teammates that the flying distance of the projectile from catapult A is the same as that of the flying projectile in catapult B, despite changing settings.

Reflection

Doing the tasks using the data we found from our DOE experiment was a good refresher in hypothesis testing and data analysis, and provided me with the opportunity to tie it together with our design of experiments data collection, which helped me to learn, understand and apply the concepts of using statistics to analyse data. It also gave me the opportunity to evaluate and provide ranges and guidelines to further analyse the data collected, as simply explaining data using graphs or charts may be inaccurate and be subjective to the user's opinion.