Hypothesis Testing

 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. Person A (Iron Man)

2. Person B (Thor)

3. Person C (Captain America)

4. Person D (Black Widow)

5. Person E (Hulk)

6. Person F (Hawkeye

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):

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 =  32(+), 26.7(-) cm Start angle = 19(+), 2(-) degree Stop angle = 90(+), 55(-) degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0):   Catapult A produces the same flying distance as Catapult B A=B     State the alternative hypothesis (H1):   Catapult A produces a different flying distance compared to Catapult B A≠B
Step 2: Formulate an analysis plan.	Sample size is 8 Therefore t-test will be used.     Since the sign of H1 is ≠, 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 = 100.3 and standard deviation = 9.00     State the mean and standard deviation of sample catapult B: Mean = 116.1 and standard deviation = 2.96     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   Therefore Ho is rejected.
Conclusion that answer the initial question	Ho is rejected, hence the H1 is accepted. Therefore, catapult A produces a different flying distance compared to Catapult B at a significance level of 5%
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Dorson: Reject Ho, accept H1 with significance level of 5% Darius: Accept Ho, reject H1 with significance level of 5% For my result, the data obtained for standard deviation was 9 (fractional). Which is relatively big, giving a bigger range of data, and that the mean would not be considered very accurate.  However, Darius' data for mean values were equal and the standard deviation for his run # was <5 which is almost half my standard deviation. Resulting an acceptable range for his value. Which made his null hypothesis valid. Since my value was quite big, the null hypothesis was rejected.  Inference made with same significance level of 5%: Due to large standard deviation, uncontrollable factors such as human factor and elasticity of the rubber band could be the reason. Another reason could be the air conditioning which may have interfered with the distance. Air resistance (without air conditioning) would be negligible since both would encounter air resistance only difference in additional air resistance from air condition can be taken into account. Speed of the release also matters and more energy would be transferred to the rubber band and this will cause more kinetic energy possessed by the ball allowing it to travel further, or travel lesser with slower release speed.

Reflection

During the tutorial, I was quite anxious as it was my first time learning this concept. The formulas given were quite difficult to interpret initially as there were different formulas for each situation. However, I was lucky that my friend took an elective: statistics for chemical & process industry. My friend taught my more in depth on how to apply certain formulas and how many tails I should look at. I am glad that I was not alone in this as it did seem daunting.

After completing the individual work, I realised how easy it was to apply the formula and interpret the hypothesis. I used to think that it was useless and challenging but now that I have completed it, I see the usefulness in it and how easy it is done.

The skills obtained from this allows me to understand how different factors affect the result and allows me to make a clearer comparison between the factors. Which would be useful in Capstone project in year 3 where we will need to know how to optimise our final product.