Hypothesis Testing

 

For this assignment, we have collected data during an experiment using catapults 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 

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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.

 

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 = 27.3 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 = 78.5cm Standard Deviation = 1.73     State the mean and standard deviation of sample catapult B: Mean = 77.5cm Standard Deviation = 5.47     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 = ± ______   Use the t-distribution table to determine the critical value of tα or tα/2 Using significance value of 5% V = 14 t0.975 = 2.145     Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 T value is within the acceptance range Therefore, Ho is Accepted.
Conclusion that answer the initial question	Since the hypothesis is accepted, Catapult A and Catapult B produces the same flying distance
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Other team members also have the same conclusion that their hypothesis was correct thus I can infer that in the widest range of settings, Catapult A and B still produce the same flying distance and thus was manufactured well

REFLECTION

All in all this hypothesis testing gave me good insight into a bit of statistics and how to compare things. This could be a useful tool to use in the future to test for things in the FYP. Overall I enjoyed learning about statistics.