HYPOTHESIS Testing

 DOE Practical Team Members

Joshua (Black Widow)

Edmund (Iron Man)

Andrew (Captain America)

Pi Ti (Hawkeye) (Me!)

Using Catapult A

Full Factorial Data Table

Link to Full Factorial Excel

Using Catapult B

Fractional Factorial Data Table

Link to Fractional Factorial Excel

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 and 32 cm

Start angle = 160 and 180 degrees

Stop angle = 60 and 90 degrees

Step 1: State the Statistical Hypotheses

State the null hypothesis (H₀):

 Catapult A produces the same flying distance as Catapult B.

 

 

State the alternative hypothesis (H₁):

Catapult A does not produce the same flying distance as Catapult B.

Step 2: Formulate an Analysis Plan

Sample size is 8.  Therefore t-test will be used.

 

Since the sign of H₁ is ≤ and ≥, a two-tailed test is used.

 

Significance level (α) used in this test is 0.01.

Step 3: Calculate the Test Statistic

State the mean and standard deviation of sample catapult A:

 Mean: 95.7 cm

Standard Deviation: 7.52

State the mean and standard deviation of sample catapult B:

 Mean: 93.3 cm

Standard Deviation: 3.39

 

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 t_α = - ______

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

3.     Two-tailed test: [ ✔ ]  Critical value t_α/2 = ± 0.005

 

Use the t-distribution table to determine the critical value of t_α or t_α/2

_{Compare the values of test statistics, t, and critical value(s),} t_α or ± t_α/2

_{v = 8+8 -2 = 14}

_{Significance 0.01 = 1- 0.01/2 = 0.995}

_{From Distribution Table, t =} ±2.977

_{Therefore Ho is rejected.}

Therefore, H1 is accepted, meaning Catapult A does not produce the same flying distance as Catapult B.

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

What inferences can you make from these comparisons?

Comparing my findings with my teammates, I found out that the majority of us rejected our null hypotheses despite using different runs meaning different values, mean flying distance and standard deviation. As this is a common trend amongst all my teammates, it is safe to assume that Catapult A does not produce the same flying distance as Catapult B.

Learning Reflection:

Hypothesis testing was a valuable chapter of my learning experience as I was able to understand more on making conclusions regarding the prototype claims. It also helped integrate my knowledge of Design of Experiment and took a step further in clarifying data and creating a better understanding on how to improve or upgrade the product/prototype. All in all, it was a bit tough to understand the steps at first but I am happy with the final results as this helped me reach another milestone on my CPDD journey.