Hypothesis testing entry

 

Week 14: Hypothesis testing entry

Contents:

1.  Introduction
2.  Full Factorial Data Table
3.  Fractional Factorial Data Table
4.  Hypothesis testing
5. Reflection

1. Introduction

For this week, we are tasked to perform hypothesis testing on the Full and Fractional factorial data collected in week 13 practical. My team members for the practical are as the following:

DOE PRACTICAL TEAM MEMBERS (fill this according to your DOE practical):

1. Person B (Thor) - Katrina 

Thor will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

2. Person C (Iron Man) - Anwar

Captain America will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

3. Person D (Black Widow) - Kieren

Black Widow will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

4. Person E (Hulk) - Jun Lin (Me)

Hulk will use Run #3 from FRACTIONAL factorial and Run#3 from FULL factorial.

2. Full Factorial Data Table

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result):

3. Fractional Factorial Data Table

Data collected for FRACTIONAL factorial design using CATAPULT B (fill this according to your DOE practical result):

4. Hypothesis Testing

Run #3

A: Full Factorial Design Data

A	B	C	R1	R2	R3	R4	R5	R6	R7	R8	Ave	Std. Dev
-	+	-	155.8	153.5	159.0	154.5	152.5	149.5	156.5	152.0	154.2	2.96

B: Fractional Factorial Design Data:

A	B	C	R1	R2	R3	R4	R5	R6	R7	R8	Ave	Std. Dev
-	+	-	157.8	153.5	158.5	154.5	150.5	149.5	159.5	153.0	154.6	3.70

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__cm Start angle = ___30__ degree Stop angle = __70___ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): Catapult A produces the same flying distance of projectile as that of catapult B.     State the alternative hypothesis (H1): Catapult A does not produce the same flying distance of projectile as that of catapult B
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 _0.025___
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: Mean = 154.6cm Standard deviation = 3.70cm   State the mean and standard deviation of sample catapult B: Mean = 154.2cm Standard deviation = 2.96cm   Compute the value of the test statistic (t):
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 = ± __2.145____   Use the t-distribution table to determine the critical value of tα or tα/2   Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 Since t = 0.223 lies in the acceptance region. Therefore Ho is __accepted_________.
Conclusion that answer the initial question	My conclusion is that both catapults produce the same flying distance.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	All of the team members came to the same conclusion as me. This tells us that both catapults produced the same distance, meaning that the manufactured products are consistent.

4. Reflection

Prior to this lesson, the only hypothesis testing I was familiar with was the formation of a hypothesis during a science experiment. I was initially overwhelmed by the new hypothesis testing concept. There were many new components, instead of creating one hypothesis like in the science experiment, I have learnt to create both a null hypothesis(H0) and an alternate hypothesis(H1). Following the creation of the two hypotheses, I must choose between the t-test, which was used for population sizes less than 30, and the z-test, which was used for population sizes greater than 30. Since for this experiment, we were using data from our previous experiment (Design of Experiment, DOE) which has a sample size of 8, I used the t-test. A two-tailed test is then chosen based on the hypothesis.

This experiment taught me more about hypothesis testing, particularly the different concepts and equations. I even felt that I had improved my hypothesis creation. I feel like this is an important lesson as hypothesis testing is essential especially for my capstone project where I have to perform data analysis.