Hypothesis Testing

Hypothesis Testing: Catapult Consistency

Introduction

Not long after bringing back half the population of the universe, the Avengers were tasked to help solve a problem older than time itself: can two things be exactly the same?

In this Hypothesis Testing entry, the following members of the Avengers participated:

1.  Cyane Low Yi Xuan (Iron Man)
2.  Clarence Wee (Thor)
3.  Salao Ryan Andrew Aguilar (Black Widow)
4.  Luacan Gene Derrick De Jesus (The Hulk)

Data Collected

Full Factorial Design

Fractional Factorial Design

For my data analysis, I will be taking a look at data from Run 8 of both Full Factorial and Fractional Factorial designs.

Data Analysis

[This template was adopted from the CPDD Blackboard page.]

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 =  27 cm Start angle = 40 degrees (average) Stop angle = 78 degrees (average)
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): At an arm length of 27 cm, with a start angle of 40 degrees and stop angle of 78 degrees, the flight distance should have no difference between each catapult. State the alternative hypothesis (H1): At an arm length of 27 cm, with a start angle of 40 degrees and stop angle of 78 degrees, the flight distance differs between each catapult.
Step 2: Formulate an analysis plan.	Sample size is 13, therefore t-test will be used. Since the sign of H1 is ≠, a two- 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: X₁ = 88.3 s₁ = 4.83 State the mean and standard deviation of sample catapult B: X₂ = 92.525 s₂ = 3.46 Compute the value of the test statistic (t): t = (88.3 - 92.525)/(4.394)(0.570) t = -1.687
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 = ± 2.201 The value of the test statistic lies within the range -2.201 <t < 2.201.   Therefore Ho is accepted and true.
Conclusion that answer the initial question	Since the null hypothesis is true, there is no or negligible difference in flight distance between catapults A and B. The catapults have been manufactured consistently, and catapult A does produce a flight distance of the projectile the same as catapult B.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	The Hulk (Derrick) had a different result from mine. He found that the test statistic was 1 below -tα/2 and therefore the null hypothesis was rejected for his set of samples, which were the data for run 3. Inference: The difference in the results shows that the assumption of human factors not affecting the flight distance is wrong.