Hypothesis Testing

 

Hypothesis Testing

21 January 2022

This week, we conducted an experiment and made use of the DOE concepts that we have learnt to conduct hypothesis testing!

My DOE Practical team members:

- Rufus How

- Alton Yau

- Ethan Chan

-Sean Tay

- ME! Heng Leon😃

Filled Full Factorial Data Table

Filled Fractional Factorial Data Table

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.

 The Scope:

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 =  ____cm

Start angle = _____ degree

Stop angle = _____ degree

Step 1: Stating the Statistical Hypothesis

 Null Hypothesis (H₀):  CATAPULT A will have the same flying distance of projectile as CATAPULT B.

Alternative Hypothesis (H₁): CATAPULT A will NOT have the same flying distance of projectile as CATAPULT B.

Step 2: Formulate an Analysis Plan

Sample size is = 16. Therefore, t-test will be used. 

Since the sign of  H₁ is  ≠ a two tailed test is used.

Significance level used in this test = 0.01

Step 3: Calculate the Test Statistic

Using Run 7 for both FULL and FRACTIONAL

For CATAPULT A:

Mean = 88.0

Standard Deviation = 3.70

For CATAPULT B:

Mean = 88.0

Standard Deviation = 3.70

Computing the test statistic using formula...

t = 0 

8 runs + 8 runs - 2 = 14

Area = 1- (0.01/2)

= 0.995

From the Student's Distribution Table,

At t = 0.995 and v = 14,

t = ±2.977

Since the t value falls within the acceptance range, we can thus accept H₀  

The Null Hypothesis stating, " CATAPULT A will have the same flying distance of projectile as CATAPULT B. " is valid at 0.01 significance level.

After concluding with other team members, we found out that the two catapults will have the same flying distance of projectiles regardless of significance levels. This suggests that the manufacturer is very consistent with his production of catapults.

Reflection

This week's practical really opened my mind to new ways to test for hypothesis. I feel that this method is really effective and efficient to collect data if you understand it well and I can definitely see myself using it in the future. However, I still get confused at times when it comes to the steps to conduct hypothesis testing, and I feel that it is something that I will need to improve on.