Hypothesis testing

 HYPOTHESIS TESTING TASK FOR INDIVIDUAL BLOG

For this assignment, you will use the DOE experimental data using the CATAPULT that you have conducted during the practical. You will use FULL FACTORIAL DATA. You are free to express yourself in your blog, but the table provided on page 2 to 7 must be followed.

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

1. Person A (Iron Man)

2. Person B (Thor)

3. Person C (Captain America)

4. Person D (Black Widow)

5. Person E (Hulk)

 

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

Iron Man will use Run #1 and Run#3. To determine the effect of projectile weight.(Ethan)

Thor will use will use Run #2 and Run#4. To determine the effect of projectile weight.(Kallysa)

Captain America will use Run #2 and Run#6. To determine the effect of stop angle. (Jing Yang)

Black Widow will use Run #4 and Run#8. To determine the effect of stop angle.

Hulk will use Run #6 and Run#8. To determine the effect of projectile weight

The QUESTION	To determine the effect of __Stop Angle__ on the flying distance of the projectile
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 is collected using the factors below: Arm length =  _28_cm Projectile weight = __0.87__ grams Stop angle = __60__ degree and __90__ degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): With an arm length of 28cm and projectile weight of 0.87g, the flying distance of projectile using stop angle of 60 degrees and 90 degrees will have no difference.    µ₂ = µ₆     State the alternative hypothesis (H1): With an arm length of 28cm and projectile weight of 0.87g, the flying distance of the projectile reduces when the stop angle increases from 60 degrees to 90 degrees.    µ₂ < µ₆
Step 2: Formulate an analysis plan.	Sample size is __16__ Therefore t-test will be used.     Since the sign of H1 is __<__, a left 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 Run # _2_:     State the mean and standard deviation of Run #_6_: 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: [ _ü_ ]  Critical value tα = - __1.761__ 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     Compare the values of test statistics, t = -71.1, and critical value(s),  tα = -1.761   Therefore Ho is _rejected as t = -71.1 lies in the rejection region_.
Conclusion that answer the initial question	Since Ho is rejected, H1 will be accepted. Hence, at constant setting for arm length and projectile weight, the flying distance of the projectile reduces when the stop angle increases from 60 degrees to 90 degrees.
Compare your conclusion with the conclusion from the other team members.	Ethan (iron man aka Person A): Since the critical value of t when there is a distribution of 95%, v=14 is 1.761. T is in the rejection region and therefore H₀ is rejected as it lies in the region of rejection. I conclude that the use of a lighter projectile would result in a larger flying distance of the projectile while using a heavier projectile would result in a shorter distance flown.  Kallysa (Thor aka Person B):  at 0.05 level of significance, an increase in projectile weight decreases flying distance in the projectile.  Weiling (Black Widow aka Person D): based on the distribution table, the critical value for t distribution of 95% and v=14 and t=2.154, t is outside of t distribution curve, therefore, the stop angle has an effect on the flying distance of the projectile.
What inferences can you make from these comparisons?	I can infer that flying distance decreases when stop angle increases. And it could also be said that flying distance increases when projectile weight reduced.
Your learning reflection on this Hypothesis testing activity	After having done this activity, it certainly does make me recall and use what I have learnt during the tutorial session for this activity.   In the previous practical, we make use of the DOE method to analyse data and see which factor has the most significance effect on the result. However, using hypothesis testing, I can make use of the data collected and analyse the data quicker. Although I find the two methods to be very useful tools, I would still prefer hypothesis testing compared to DOE as to me DOE’s main drawback is its complexity.   From this session, I have learnt some important things on hypothesis testing, like Hypothesis testing is the process used to evaluate the strength of evidence from the sample and provides a framework for making determinations related to the population. So, if I want to determine if a statistical hypothesis is true, all I have to do is follow the steps:   Step 1: State your null and alternate hypothesis (Ho and H1) Step 2: Collect data. Step 3: Perform a statistical test. Step 4: Decide whether to reject or fail to reject your null hypothesis. Step 5: Present your findings.   With this, I hope to implement this new skill I have learnt in future such as Capstone project and internship.