Hypothesis Testing

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Overview

Welcome back to my blog ! This week's focus is on Hypothesis Testing on the catapult experiment that we did in class.

Here are the DOE team members:

1. Nander (Iron Man)

2. Tzer (Thor)

3. Ashwati (Captain America)

4. Nikkisha (Black Widow)

5. Daryl (Hulk)

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result)



Data collected for FRACTIONAL factorial design using CATAPULT B (fill this according to your DOE practical result): 


Iron Man will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

Thor will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.

Captain America will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

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

Hulk will use Run #4 from FRACTIONAL factorial and Run#4 from FULL factorial.

Hawkeye 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 = 31 cm

Start angle = 20 degree

Stop angle = 60 degree

 

Step 1:

State the statistical Hypotheses:

State the null hypothesis (H0):

 

H0: µ1 = µ2

 

Catapult A and Catapult B produces equal projectile distance

 

State the alternative hypothesis (H1):

 

H1: µ1 ≠ µ2

Catapult A and Catapult B does not produce equal projectile distance

 

 

Step 2:

Formulate an analysis plan.

Sample size is 16.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:

 

Mean: 100.4

Standard Deviation: 2.93

 

State the mean and standard deviation of sample catapult B:

 

Mean: 118.8

Standard Deviation: 3.15

 

 

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: [ __ ]  Critical value tα = - ______

2.     Right-tailed test: [ __ ]  Critical value tα =  ______

3.     Two-tailed test: [ ✓ ]  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

Since the value -11.32 lies in the rejection zone 

Therefore, Ho is rejected.

 

 

Conclusion that answers the initial question

 

Catapult A and B does not produce the same projectile distance at the significant level of 0.05 

 

 

 

 

Compare your conclusion with the conclusion from the other team members.

 

What inferences can you make from these comparisons?

 

After looking through my group mate's results, I have concluded that their results were similar to mine. Their conclusion was also that the manufacturer had inconsistency in the distance between the two different catapults.

Reflection

At the start of the lesson, Hypothesis Testing seemed scary. There were a lot of foreign technical terms that I have never ever came across. Hence, it was hard to understand what was going on. I could barely start on any of the 4 questions in the beginning. However, after clarifications with my lecturer, I slowly got the hang of what Hypothesis Testing is and I could carry on with my work. Throughout this process, it made me realize that such methods can be very beneficial for me, in my upcoming projects or lab works. To conclude, I am happy I was taught about this method and I am sure that I will be using this method again and again.

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