Hypothesis testing

DOE PRACTICAL TEAM MEMBERS:

1. Person A (Iron Man): Zelene

2. Person B (Thor): Junheng

3. Person C (Captain America): NIL

4. Person D (Black Widow): Zhiwei

5. Person E (Hulk): Ambrose

6. Person F (Hawkeye): Haziq

The full factorial data table is as shown below. This is the data collected for full factorial design using CATAPULT A

The fractional factorial data table is as shown below. This is the data collected for fractional design using 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 = 28.5cm Start angle = 3 degrees Stop angle = 20 degrees

Steps to accepting hypothesis:

Step 1: State the statistical hypotheses	State the null hypothesis (H0): CATAPULT A produces the same flying distance of projectile as that of CATAPULT B. State the alternative hypothesis (H1): CATAPULT A does not produce the same flying distance of projectile as that of CATAPULT B.
Step 2: Formulate an analysis plan	Sample size is 8, 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 sample catapult A: Mean of catapult A: 150.4cm Standard deviation: 2.42   State the mean and standard deviation of sample catapult B: Mean of catapult B: 148.8cm Standard deviation: 2.62   Compute the value of the test statistic (t):
Step 4: Make a decision based on result	Type of test (check one only) 1.     Two-tailed test       Critical value tα/2 = ± 2.145   Compare the values of test statistics, t, and critical value(s), tα or ± tα/2   t value of 1.1868 falls between acceptance of ± tα/2 values. Therefore, H0 is accepted.

Conclusion:

CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

Discussion:

Comparing my conclusion with the conclusion from other team members,

Person A (Iron Man): Zelene
CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

Person B (Thor): Junheng
CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

Person D (Black Widow): Zhiwei
CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

Person E (Hulk): Ambrose
CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

Person F (Hawkeye): Haziq
CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

What inferences can you make from these comparisons?
All the members in the group has concluded that catapult A produces the same flying distance of projectile as that of catapult B. Inferring from our hypothesis claims, Catapult A very much produces the same flying distance of projectile as that of catapult B after forming a hypothesis test with multiple runs. This means that the manufacturing quality of catapult A and B is around the same as well, because they produce the same flying distance of projectile when the same level of factor is used.

Reflection:

From the lessons regarding hypothesis testing, I have understood that hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. This analysis depends on the nature of the data used and the reason for the analysis. Hypothesis testing is then used to assess the plausibility of a hypothesis by using a sample data from the population. In a simplified real life example, if you were to create a drug that is effective in treating headaches, unless you can replicate the same result with the same drug reliably, no one would take your results seriously.

I still find it easy to mix up the hypothesis Ho and H1 as well as between a one tailed and two tailed approach. Hypothesis testing is still new to me, and it can be difficult to differentiate between a two tailed approach and a one tailed approach. This is a good opportunity to continue brushing up my skills on forming hypotheses for scientific experiments and collecting data from the population size.