HYPOTHESIS Testing

HYPOTHESIS Testing

Halo! Welcome back to yet another blog. This week, I had learnt on Hypothesis Testing!✌

DOE Practical Members:

Member	Hero	Run #
Steward	Iron Man	Run #2 of Fractional and Full Factorial
Wayne	Thor	Run #3 of Fractional and Full Factorial
Jiayu	Captain America	Run #5 of Fractional and Full Factorial
Xin Ni	Black Widow	Run #8 of Fractional and Full Factorial
Nick	Hulk	Run #3 of Fractional and Full Factorial
-	Hawkeye	Run #8 of Fractional and Full Factorial

Full Factorial data table:

Fractional Factorial data table: 

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 cm

Start angle = 30 degree

Stop angle = 55 degree

Step 1: State the statistical Hypotheses

Null Hypothesis (H₀): Both Catapult A and B produces the same flying distance.

Alternate Hypothesis (H₁): Catapult A and Catapult B does not produce the same flying distance.

Step 2: Formulate and Analysis Plan

Sample size is 16, which is less than 30, therefore t-test will be used.

Since the sign of H₁ is"≠", a two-tailed is used.

Significance level is 0.05.

Step 3: Calculate the Test Statistic

Catapult A	Catapult B
x̄1: 108.9cm	x̄2: 110.6cm
S1: 2.20cm	S2: 2.03cm
n1: 8	n2: 8
α= 0.05

Computing the value of the test statistics(t):

Step 4: Make a decision based on the result

It is a two-tailed test, therefore critical value t_α/2 = ± 0.025

0.1 - 0.025 = 0.975

From Appendix, at 0.05 level of significance, V=14, t_0.975 = ± 2.145

Test statistics (-1.5) falls within the acceptance region, thus, H₀ is accepted.

Step 5: Conclusion that answers the initial question

At 0.05 level of significance, both catapults produces the same flying distance.

Comparison of Answer:

Member	Run #	Conclusion
Steward	Run #2 of Fractional and Full Factorial	Both catapults produce the same flying distance.
Wayne	Run #3 of Fractional and Full Factorial	Both catapults produce the same flying distance.
Jiayu	Run #5 of Fractional and Full Factorial	Both catapults produce the same flying distance.
Xin Ni	Run #8 of Fractional and Full Factorial	Both catapults produce the same flying distance.
Nick	Run #3 of Fractional and Full Factorial	Both catapults produce the same flying distance.

At a rather consistent small standard deviation and a constant significance value of 0.05, all the t statistics falls under the Acceptance region, where the H₀ is accepted. 

At significance level of 0.05, there is more room for proving, and it is a less stringent method. Therefore, at 0.05 level of significance, at little standard deviation, all the conclusions for the runs are the same.

Inferring from the results from my teammates, I can conclude that catapults manufactured will always produce the same flying distance.

Reflection:

Hypothesis Testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.

When I was first taught on this during a Monday morning lesson, it was a bit confusing and was unsure on what to do. After consulting my teacher and my classmates for help, I had begun to slowly understand on how I can properly do the necessary calculations to hypothesize on the assignment questions. 

This technique can be very useful in our FYP. When in need of proving a hypothesis, we can always use this method to show our hypothesis.