Hypothesis Testing
Week 15
This week, we learnt how to do hypothesis testing, and sadly, it is our last tutorial material for this term. For this blog entry, we have to do the hypothesis testing for the DOE practical that we did a few weeks ago.
For the practical that we had a few weeks back, my groupmates were,
-Zhi Wei (Black Widow, Person D)
-Jun Heng (Thor, Person B)
-Haziq (Captain America, Person C)
-Ambrose (Hulk, Person E)
-Myself, Zelene (Iron Man, Person A)
Full Factorial
|
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 = __28.5__cm Start angle = __5___
degree Stop angle = ___49__
degree
Since I am Iron Man, Person
A, I would use Run 2 from fractional factorial and run 2 from full factorial.
|
|
Step 1: State the
statistical Hypotheses: |
State the null hypothesis
(H0):
H1=H0
Catapult A and B will produce
the same flying distance
State the alternative
hypothesis (H1):
H1≠H0
Catapult A and B will produce different flying distance
Let Catapult A be from full factorial and B be from
fractional factorial |
|
Step 2: Formulate an
analysis plan. |
Sample size is __8__
Therefore t-test will be used.
Since the sign of H1
is __≠__, a left/two/right
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: Mean: 150.4 Standard Deviation: 2.42 State the mean and standard deviation of sample catapult B: Mean: 151.9 Standard Deviation: 2.77  |
|
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 = ± ______ Use the t-distribution
table to determine the critical value of tα or tα/2 From the t-distribution table, at t0.975 = 2.145 at V=22 Compare the values of test statistics, t, and critical value(s), tα or ± tα/2  Since t= 1.079 and is lesser than t0.975=2.145 Therefore, H0 is accepted and H1 is rejected
|
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Conclusion
that answer the initial question |
|
|
Compare your
conclusion with the conclusion from the other team members. What
inferences can you make from these comparisons? |
My conclusion is that both catapults A and B have the same flying distance. Teammates' Conclusion Zhi Wei- Both catapults A and B have the same flying distance Haziq- Both catapults A and B have the same flying distance Jun Heng- Both catapults A and B have the same flying distance Ambrose- Both catapults A and B have the same flying distance Inference: This shows that all of us got the same result and that is both catapults A and B have the same flying distance. Hence, it can be taken from all of our conclusions, that both catapults A and B have the same flying distance and that the company that manufactured the catapults are consistent. |
The main objective of this blog is to allow us to have some practice on hypothesis testing and to allow us to come to a conclusion after collecting all the data. This is also a continuation of the previous blog, the one on Design of Experiment, and that after collecting all the data according to the DOE, we can then use the this method, the Hypothesis testing to make sense of the data that we collected and to come to a conclusion. This also made me more familiar with the method used for hypothesis testing and that this skill would be very helpful in Year 3 when we do our final year project.
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