Hypothesis Testing

In this blog, I will be documenting my learning experience on Hypothesis Testing.

Content:

1. Context of the assignment

2. How to apply Hypothesis Testing

3. Learning reflection

4. Reference

CONTEXT OF THE ASSIGNMENT

For this assignment, I will use the DOE experimental data using the CATAPULT that we have conducted during the practical. I will use FULL FACTORIAL DATA. 

DOE PRACTICAL TEAM MEMBERS (fill this according to your DOE practical):

1. Hannah (Iron Man)

2. Justin (Thor)

3. Myself (Captain America)

4. Jun Hao (Black Widow)

5. Keith (Hulk)

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result):

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

HOW TO APPLY HYPOTHESIS TESTING

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 the different users will not have any effect on the flying distance of the projectile. Flying distance for catapult A is collected using the factors below: Arm length =  33cm Projectile weight = 0.86 grams Stop angle = 15 degree and 49 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): State the alternative hypothesis (H1):
Step 2: Formulate an analysis plan.	The sample size is 8. Therefore t-test will be used. Since the sign of H1 is ±, a two-tailed test is used. The significance level (α) used in this test is 0.05.
Step 3: Calculate the test statistic
Step 4: Make a decision based on result	Type of test (check one only) Left-tailed test: [ __ ]  Critical value tα = - ______ Right-tailed test: [ __ ]  Critical value tα =  ______ Two-tailed test: [✅]  Critical value tα/2 = ± 2.145 (for v=14) Use the t-distribution table to determine the critical value of tα or tα/2 Based on the illustration above, Ho is rejected.
Conclusion that answer the initial question	At 0.05 significance level, the table value of t.975 = ±2.145 for v = 14. Since the test statistic t = ±2.81 lies in the rejection region, the null hypothesis is rejected. The alternative hypothesis is accepted.  Hence, at a 0.05 significance level, there is a significant effect of the stop angle on the flying distance of the projectile. Therefore, reducing the stop angle from 15 degree to 49 degree, will change the flying distance of the projectile while the arm length and projectile weight remain constant.
Compare your conclusion with the conclusion from the other team members.	Black Widow’s result: Reducing the stop angle from 15 to 49 degree does not change the flying distance of the projectile.  (no significant effect)
What inferences can you make from these comparisons?	I do think the stop angle has a significant effect on the flying distance of the projectile as during the DOE practical, we realised that when we increased the stop angle, the flying distance was greatly reduced.  From the illustration above, I can infer that when arm length and projectile weight remains constant. When the stop angle increases from LOW (-) to HIGH (+), the flying distance reduces from 78.8cm to 73.4cm. From the illustration above, this is the set of data that Jun Hao used and I can infer that the stop angle has a significant effect on the flying distance of the projectile. This is because when the stop angle increases from LOW (-) to HIGH (+), the flying distance increases from 68.4cm to 71.6cm which doesn’t make sense because when we increase the stop angle, the flying distance should decrease. Hence, we may measured the distance wrongly.  Nonetheless, this still proves that the stop angle has a significant effect on the flying distance of the projectile.

LEARNING REFLECTION

I was very confused😰 and lost during the tutorial session because I couldn't comprehend the information. I'm a slow learner so it takes time for me to absorb all the information.

I learned that hypothesis testing is helpful👍 as hypothesis testing is the process used to evaluate the strength of evidence from the sample and provides a framework for making determinations related to the population or the problem statement. It is used after applying DOE to further investigate the relationship and significance between each parameter.

During our tutorial session, Dr Noel also mentioned that hypothesis testing is used after applying DOE and I think was because the purpose of hypothesis testing is to test whether the null hypothesis (there is no difference, no effect) can be rejected or approved. If the null hypothesis is rejected, then the alternative hypothesis can be accepted.

I would say it is similar to the concept of probability which I learned in secondary school. However, it is a little advance and in-depth.🎉

Reference

Ali Ashasi-Sorkhabi, Bryan Tolson, Liping Fu, Giovanni Cascante, September 2019. Experimental Design and Hypothesis Testing [online]. Available at: https://uwaterloo.ca/civil-environmental-engineering/sites/ca.civil-environmental-engineering/files/uploads/files/experimental_design_and_hypothesis_testing_gc.pdf [2 February 2023].