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:

1. Person A (Iron Man) - Zelene

2. Person B (Thor) - Jun Heng

3. Person C (Captain America) - Haziq

4. Person D (Black Widow) - Zhi Wei

5. Person E (Hulk) - Ambrose

6. Person F (Hawkeye)

Data collected for FULL factorial design using CATAPULT A

Data collected for FRACTIONAL factorial design using CATAPULT B 

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

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 =  __28.5__cm Start angle = __20___ degree Stop angle = __90___ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): There is no difference between the flying distance of projectile of CATAPULT A and CATAPULT B. X̅A=X̅B   State the alternative hypothesis (H1): There is a difference between the flying distance of projectile of CATAPULT A and CATAPULT B. X̅A≠X̅B
Step 2: Formulate an analysis plan.	Sample size is   8   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: X̅A=95.1   sA=2.4     State the mean and standard deviation of sample catapult B: X̅B=94.1   sB=6.51     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: [ _ t.95 _ ]  Critical value tα = - 1.716    2.    Right-tailed test: [ _ t.95 _ ]  Critical value tα = 1.716 3.    Two-tailed test: [ _ t.975 _ ]  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 answer the initial question	There is a difference between the flying distance of projectile of CATAPULT A and CATAPULT B at a significance level of 0.05.
Compare your conclusion with the conclusion from the other team members What inferences can you make from these comparisons?	All team members get the same conclusion which is there is no difference between the flying distance of projectile catapult A and catapult B at a significance level of 0.05.  My team members and I obtained the same conclusion which is accepted null decision at the significance level of 0.05. In my opinion, if we choose different significance levels, we may obtain different conclusions.

Reflection

I found this task is quite easier for me to complete. It was because I had learnt hypothesis testing in my elective module (Statistics For Chemical And Process Industry). Hypothesis testing was an important statistical technique to determine a possible conclusion from 2 different hypothesis statements. This task helped me to enhance my memory towards this knowledge I learned before and it was useful for me to do revision again. I hope I can apply it very well in my final year project.