Hypothesis Testing

 Hypothesis Testing

In this blog entry, i will be using the data obtained from the previous practical Design of experiment to perform FULL and Fractional Factorial.

During the practical, my group comprised of :

• Alton Yau
• Heng Leon
• Ethan Chan
• Sean Tay
• Rufus How

Full Factorial

Fractional Factorial

The Question

The catapult manufacturer needs to determine the consistency of the products they manufactured. Therefore, they want to determine whether Catapult A produces the same flying distance as catapult B.

The scope

The Human factor is assumed to be negligible. Hence different user will not have any effect on the flying distance of the projectile.

Flying distance for catapult A and B is collected based on the factors:

Arm Length = _____cm

Start Angle = ______degree

Stop Angle = ______degree

Step 1: Stating the statistical hypothesis

Null Hypothesis: The projectile from catapult A will travel the same distance as that from catapult B

Alternate Hypothesis: The projectile from catapult A will not travel the same distance as that from catapult B

Step 2: Formulate an analysis plan

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

Since the size of H1≠ a two tailed test will be used

Significance level used in this case is 0.01

Using run 2 from Full and Fractional factorial

Step 3: Calculate the test statistic

Catapult A

Mean = 150.1

Std = 4.51

Catapult B

Mean = 150.1

Std = 4.51

Computing the value of test statistic

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 the null hypothesis.

The null hypothesis" the projectile from catapult A will travel the same distance as that from catapult B" is therefore valid at a significance value of 0.01.

After comparing the with other group members, it can be seen that the distance travelled by the projectile from both catapult A and B is the same even at different significance level. Hence, it can be concluded that the catapult created by the manufacturer is indeed consistent and well made. 

Reflection

This activity served as a good way to test my understanding on hypothesis testing and how it is done in the real world. The 5 steps is very systematics and easy to follow and it helped me better understand the concept of hypothesis testing. That being said, I feel that my understanding on hypothesis testing is not developed fully and therefore, it is a point that i should try my best to improve my skills in hypothesis testing.