Hypothesis Testing

 

HYPOTHESIS TESTING TASK FOR INDIVIDUAL BLOG

 

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. Kenny (Iron Man)

2. Sebastian (Thor)

3. Shin Shing (Captain America)

4. Danial (Black Widow)

5. Esen (Hulk)

6.  Jun ying(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):

Iron Man will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

Thor will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

Captain America will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

Black Widow will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

Hulk will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

Hawkeye 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 =  27cm Start angle = 0 degree Stop angle = 60 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): H0=H1   State the alternative hypothesis (H1): H0 ≠H1
Step 2: Formulate an analysis plan.	Sample size is 8 (n<30) 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 sample catapult A: Mean(x̄)= 159.4 Standard deviation(σ)= 3.74   State the mean and standard deviation of sample catapult B: Mean(x̄)= 161.6 Standard deviation(σ)= 3.81 Compute the value of the test statistic (t): V= 8+8-2=14 σ=4.0358 t=-1.09
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  Since t is -1.09 which lies in between ± 2.145. Therefore Ho is acceptable.
Conclusion that answer the initial question	Since t is -1.09 which lies in between -2.145 to 2.145,  Ho is acceptable the flying distance produce by both catapult A and catapult B are similar. Therefore, this means that the alternative hypothesis H1 is rejected.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	After comparing my conclusion with the conclusion from the other team members I find that our results are not the same. For example, there are team members where there null hypothesis is true which is same as mine and there are also team members where their alternative hypothesis is true. After comparing the results of my team members, I can infer that different will result in different conclusion due to the difference in factors used. However, even though different run number is used, similar conclusion may produced. For example, I did run #2 and my team member who did run #3 have the same conclusion which null hypothesis is being accepted.

Reflection

During this lesson, I learnt that Hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses. With the use of hypothesis testing, I am able to compare and determine whether the sample data collected is consistent with my hypothesis which then able to reject the hypothesis. Also, during the lesson learned the different types of decision errors and the steps involved in Hypothesis Testing. Through the exercise given, I learnt the difference between null hypothesis and alternative hypothesis and also how they are applied during hypothesis testing. Additionally, I learnt how to calculate the test statistic of comparing sample mean and population mean and comparing between two sample mean. Next, I learned the decision rule for accepting or rejecting null hypothesis by defining the means of accepting region. After learning all of these, we were give some practice question for us to practice on what we have just learned. Through the practice question, I have deeper understanding of hypothesis testing by applying it to solve problems. 

After we have submitted our answer for the practice question and shows that we are competent in completing the task for hypothesis testing, our lecturer then released the assignment for hypothesis testing. For this task we are required to perform hypothesis testing based on the practical result that we have obtained from Design of experiment on the flying distance of catapult with varying factors. What I remembered the most from this practical is that we have to spilt ourselves randomly into different groups which I felt uncomfortable as I need to group with people that I have little understand and not close to. But we are able to work together as a group to complete and obtain the data needed for the practical on design of experiment which then the data is being used here for hypothesis testing. Through the previous practical I was required to work with others that I am not familiar with which improves my communication skills.

The task of hypothesis testing is important as it gives a better understanding of hypothesis by applying it. Also, Hypothesis testing is the procedures used by experimenters or researchers to accept or reject statistical hypotheses. With the use of hypothesis testing, I am able to compare and determine whether the sample data collected is consistent with my hypothesis which then able to reject the hypothesis. Hence, Hypothesis testing is important in decision making. To me, the most interesting part of this practical is the part where we did hypothesis testing our determine whether our experiment data is acceptable or not acceptable. This task is useful for the project in CP5070 as this task improve my competencies in applying hypothesis testing for the next practical in CP5070 if required.

I used to think that hypothesis testing is complicated and hard to as when my lecturer is explaining the concept of hypothesis testing I do not really understand it. Now, after having a deeper understanding and applying hypothesis testing, I have more confident in applying hypothesis testing on future experiment data . So next I am able to apply hypothesis testing in for future experiment, Final year project and during internship if needed.