Hypothesis Testing

 

HYPOTHESIS TESTING TASK

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

1. Katrina (Thor)

2. Anwar (Iron Man)

3. Kieran (Black Widow)

4. Jun Lin (Hulk)

 Data collected for FULL factorial design using CATAPULT A

Data collected for FRACTIONAL factorial design using CATAPULT B

Since I chose Iron Man, I will use Run #2 from FRACTIONAL factorial and Run #2 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 = 34cm

Start angle = 0 degree

Stop angle = 70 degree

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 small 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: 142.2

Standard Deviation: 5.14

 

State the mean and standard deviation of sample catapult B:

Mean: 143.2

Standard Deviation: 4.64

 

Compute the value of the test statistic (t):

 

 

 

Step 4: Make a decision based on result

Type of test:

Two-tailed test, thus critical value 0.05_/2 = ± 0.025

1 – 0.025 = 0.975

Using t-distribution table, critical value of t_0.975 = ±2.145

Since -2.145 < -0.382 < 2.145, therefore -0.382 is within the accepted range, hence H₀ is accepted.

 

Conclusion that answer the initial question

At 0.05 significance level, Catapult A and Catapult B will produce the same flying distance.

 Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?

The conclusion gathered from the other team members is that there is no difference in the flying distance from both catapults. Thus, it can be inferred that the consistency of the products manufactured is high, and there are no quality control issues between different catapults of the same model.

Reflection

Overall, hypothesis testing is actually quite simple once you are familiar with it. Initially, it seemed very complicated. However, with practice it became a lot easier than it looked. I feel like it is a very important skill, especially in analysing the validity of a claim. On a larger scale, it can be used for analysing quality consistency in products.