HYPOTHESIS TESTING 🔎.🔍

In this Hypothesis testing practical lesson, since there were 5 groups for CPDD class, Dr Noel used the group generator to make 4 groups. Thus, my group members for this practical is different. They are Derrick, Ryan Andrew, and Clarance. Since there were 4 people in the group, we split the group into 2, whereby me and Ryan Andrew did the fractional factorial, while Derrick and Clarance did the full factorial. 

Group members:

1. Cyane (Iron Man)

2. Clarance (Thor)

3. Ryan Andrew (Black Widow)

4. Derrick (Hulk)

For this experiment, the 3 factors used are,

1. Arm length

2. Start Angle 

3. Stop Angle

Since the 2 separate groups are using a different catapult, we also chose different high and low values for start and stop angles.

Filled Full factorial table by Derrick and Clarance (catapult "A"):

 Filled Fractional factorial by Ryan Andrew and I (catapult "B"):

The Question:

The catapult (the ones that were sued 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.

Step 1: State the statistical Hypothesis

Null Hypothesis (H₀): (=)

The flying distance of projectile is the same for both catapult "A" and "B".

Alternative hypothesis (H₁): (≠)

The flying distance of the projectile is not the same for both catapult "A" and "B".

Step 2: Formulate an analysis plan

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

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

Significant level (α) used n this test is 5%. (t = 0.975)

Step 3: Calculate the test statistic

State the mean and standard deviation of sample catapult "A"

Mean: 142.4

Standard deviation: 4.54

State the mean and standard deviation of sample catapult "B"

Mean: 107.85

Standard deviation: 1.86

Compute the value of the test statistic (t): 

By using the formula given,

σ = 

σ = 3.71

v = 8 + 8 - 2

v = 14

t = (142.4-107.85)/3.71(0.5)

t = 34.55/ 1.855

t = 18.625

Step 4: Make a decision based on the results

Type of test:

Two-tailed test:

Critical Value t_α/2 = ± 2.145 

(from distribution table, v= 14, and t= 0.975)

Using the t distribution table to determine the critical value of t_α/2,

Compare the values of test statistics, t, and critical value(s), ± t_α/2. 

Therefore, (H₀) is rejected.

Conclusion that answer the initial question:

The flying distance of the projectile is not the same for both catapult "A" and "B". Because the t value is more than 2.145. Thus, it is at the rejected range using the two-tailed diagram.

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

What inferences can you make from these comparison?

By comparing my calculated results with my other team members, the t value found for my run and their run was way too different and that we have different conclusions for our different runs. From this, I can infer that there might be an error during the our experiments which caused my t value to differ so much than expected. Thus, run 2 is not reliable.

Reflection:

To summarize this experiment, we used different factors and observe their significance. 

This practical is important because it helps us identify which factor affects the flying distance of the projectile the most (most significant), by using the factorial design, both full ad fractional. The most interesting part of this experiment was the part where we choose our own high and low values/parameters. As we have to make sure that we would be able to see a change in the data collected and come up with our own conclusion. This is useful in CP5070 as when we start doing our product development, we will need to test it out and that this could show which is the most significant factor and we could amend it accordingly. This hypothesis testing is also important and useful to CP5070 as it helps us check whether our product is in the acceptable range.

I used to think that hypothesis testing is really difficult to understand as there are a lot of calculations. Now I think that once I understand and have more practice, I am able to do and conclude the hypothesis testing myself. So next I will apply this hypothesis testing skills into my group's product development project.