Hypothesis Testing

Hypothesis Testing

For this weeks blog, I will be talking about what I have learned about hypothesis testing by applying it to the data that I had used in the previous blog about Design of Experiment (DOE). The data was collected during the DOE practical where we had measured the distance travelled by the projectile using different catapult configurations. My group members consists of:

1. Tzer (Thor)
2. Nander (Iron Man)
3. Daryl (Hulk)
4. Nikkisha (Black Widow)
5. Ashwati (Captain America)

The data that had been collected for both Full Factorial and Fractional Factorial using 2 different catapults can be found below:

Figure 1: Full Factorial Data Table

Figure 2: Fractional Factorial Data Table

I have selected to perform hypothesis testing on Run#4

The Question that is to be answered using hypothesis testing is whether the different catapults are consistent i.e. they produce an identical range of flying distance under the same configuration.

The scope of the test is that human factor is assumed to be negligible where the different users operating the catapults will not have any effect on the flying distance of the projectile. For Run#4, the flying distance for catapult A and catapult B are collected with both catapults having the same configuration of:

Arm Length = 31cm

Start Angle = 20 Degrees 

Stop Angle = 90 Degrees

Step 1

The null hypothesis Ho is that the distance travelled by the projectile is the same for both catapults and hence both catapults are identical.

The alternative hypothesis H1 is that the distance travelled by the projectile is different for both catapults and hence both catapults are NOT identical.

Step 2

Since the sample size is 16 and the sign of H1 is NOT ≠, a two-tailed t-test with a significance level (𝞪) of 0.05 will be used.

Step 3

For Catapult A:

• Mean (𝑿1) = 100.6cm
• Standard Deviation (s1) = 2.93cm
• Sample Size (n1) = 8

For Catapult B:

• Mean (𝑿2) = 118.8cm
• Standard Deviation (s2) = 3.15
• Sample Size (n2) = 8

Figure 3: Formulas used for Step 3

t = -11.193

v = 14

𝞼 = 3.25

Step 4

Using the t-distribution table, the critical value t𝞪/2 = ±2.145

Figure 4: Two-Tailed Graph for Step 4

Since the value of t = -11.93 lies within the rejection zone created by t𝞪/2 = ±2.145, the null hypothesis Ho is rejected.

Conclusion

From analysing the data of Run#4, it can be concluded that catapult A does not produce the same projectile flying distance as catapult B and hence they are not consistent enough to be up to standard at a significance level of 0.05.

Comparisons and Inferences

Based on the answers obtained from Nander who had performed hypothesis testing on Run#2 and Ashwati who had performed hypothesis testing on Run#5. My conclusion that catapult A and catapult B do not produce the same projectile flying distance under the same configuration is proven to be true as they had also come to the same conclusion of rejecting Ho. It can hence be inferred that the flying distance of the projectile from the 2 catapults will be different regardless of the configuration used, even if they are using identical configurations.

Reflection

During the lesson on hypothesis testing, I was initially taken aback as the process seemed very foreign and complex to me. However, practice makes perfect, and we were tasked with doing some practice questions on hypothesis testing which we would have to submit by the end of the day. I was completely lost and did not even know how to start any of the 4 questions, it was only after the lecturer had gone through the first 3 questions did I get the hang of it and managed to solve the 4th question without his guidance. I can now confidently say that I have understood the hypothesis testing process after completing those practice questions and this blog and that it is actually not as complex and hard to do as I had previously thought. 

Overall, I feel like this will definitely come in handy in my Final Year Project as I will be bound to have to test out the prototype  and this will surely be one of the methods that will be used. This skill may also be of help later on in life after I have graduated from poly be it in my future job or in university.