Hypothesis Testing

Hello and welcome back to my blog. This post is based on the final topic that I learned for CPDD known as Hypothesis Testing. This post covers my using hypothesis testing with the results obtained from my DOE practical that was covered a few weeks ago on my blog.

DOE PRACTICAL TEAM MEMBERS:

1. Hannah (Iron Man)

2. Justin (Thor)

3. En Ting (Captain America)

4. Jun Hao (Black Widow)

5. Keith (Hulk)

 

Data collected for FULL factorial design using CATAPULT A :

Iron Man will use Run #1 and Run#3. To determine the effect of projectile weight.

Thor 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

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 = 12.5cm Projectile weight = 2.05grams Stop angle = 15 degree and 49 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 of the projectile.     State the alternative hypothesis (H1): The stop angle has a significant effect on the flying projectile.
Step 2: Formulate an analysis plan.	Sample size is 2 Therefore t-test will be used.     Since the sign of H1 is ≠, a two 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 #4: Mean = 68.4 Standard deviation(σ) = 5.15 State the mean and standard deviation of Run #8: Mean = 71.6 Standard deviation(σ) = 4.84   Compute the value of the test statistic (t): t = ±1.198 v = 8 + 8 – 2 = 14 σ= 5.342
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 Accepted.
Conclusion that answers the initial question	H0 is accepted, which means that is H1 rejected. This means that the stop angle does not have a significant effect on the flying distance of the projectile.
Compare your conclusion with the conclusion from the other team members.	According to my groupmate En Ting, who also used this table to find the effect of stop angle on the flying distance of the projectile, her conclusion differs from mine. Her conclusion stated that changing the stop angle from 15 to 49 degrees will have a significant effect on the flying distance of the projectile.
What inferences can you make from these comparisons?	Some inferences I can make from this comparison are that the effects of the stop angle may differ according to other factors such as arm length and projectile weight as well. This means that, in our case, changing the projectile weight affects the results of the stop angle on the flying distance of the object. Another inference is that even though we had used the same set of data, the effects on other factors are somewhat inconclusive as can be seen from our comparison. This means that we cannot conclude what each factor does to the flying distance of the object independently as the factors seem to collide with each other.
Your learning reflection on this Hypothesis testing activity	This hypothesis testing activity has allowed me to better understand the importance of the topic as well as how to conduct it more effectively.  When first learning hypothesis testing in class, it took me a very long to fully understand what it was about and how to conduct it on the practice questions we were given. It took a lot of asking around my friends, reading up on it and watching videos on the topic to give me a semblance of understanding of the topic. Even then it took me a while to complete the practice questions properly. This activity has raised my understanding of the topic by quite a large margin.  Moreover, having to compare the results of the study of the same set of results has allowed me to better realise the importance of this topic and why it should be implemented when doing projects. Overall, my feelings on this topic are quite positive as I can now see it as an important thing to know for future use.

This brings this blog post to an end. The next post will likely be the last as it will cover the last project in CPDD. Until next time!