Hypothesis Testing

In week 14, we learnt about Hypothesis Testing. In this blog, I will be determing whether a factor from the DOE practical affects the flying distance of projectile.

My DOE team members are

1. Yeung Juen (Iron Man)

2. 2. Mavis (Thor)

3. Isabelle (Captain America)

4. Alvin (Black Widow)

Data collected for Full Factorial Design from DOE Practical is shown in the table below.

Iron Man will use Run #1 and Run #3. To determine the effect of projectile weight. Thor will use will use Run #2 and Run #4. To determine the effect of projectile weight. Captain America will use Run #2 and Run #6. To determine the effect of stop angle. Black Widow will use Run #4 and Run #8. To determine the effect of stop angle. Hulk will use Run #6 and Run #8. To determine the effect of projectile weight.

Table for Captain America & Black Widow

​The QUESTION	​To determine the effect of stop angle on the flying distance of the projectile
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 is collected using the factors below: Arm length = 75 cm Projectile weight = 0.85 grams and 20 grams Stop angle = 15 degree and 30 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The stop angle does not have a significant effect on the flying distance when the arm length is 75cm and projectile weight is either 0.85g and 20g. State the alternative hypothesis (H1): The stop angle has a significant effect on the flying distance when the arm length is 75cm and projectile weight is either 0.85g and 20g.
Step 2: Formulate an analysis plan.	​Sample size is 16. 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 Run #2: Mean: 70.9 cm Standard Deviation: 1.31cm State the mean and standard deviation of Run #8: Mean: 77.4cm Standard Deviation: 2.93cm Compute the value of the test statistic (t): v = 8 + 8 - 2 = 14 Σ = 2.42 t = ± 5.3719
​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	Since Ho is rejected, when the arm length is 75cm and projectile weight is either 0.85g and 20g, there is a difference in the flying distance when the stop angle is changed.
Compare your conclusion with the conclusion from the other team members.	​My groupmate, Alvin, who got t = ± 1.5323. Hence, his Ho is accepted meaning that there is no significant change in fying distance when the stop angle is changed.
What inferences can you make from these comparisons?	​The runs used will affect the conclusions we get from the hypothesis testing. I can also infer that the results we got from the DOE practical are inconsistent. Hence, it is unreliable. It could also be due to the projectile weight having a significant effect as my hypothesis included the weights of 0.85 grams and 20 grams while Alvin used the runs with only 2 grams.
Your learning reflection on this Hypothesis testing activity	​Hypothesis testing allowed for us to prove whether a hypothesis is proven true in the most accurate and reliable way. Comparing the results calculated with the accepted and rejected region is something that is more accurate as compared to testing a product or experiment over and over again. This is something I can integrate into my Capstone project as it can help in telling me whether a certain factor will affect the product. From that, we can make further improvements until we are content.