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): Ryan

2. Person B (Thor): Haiteng

3. Person C (Captain America): Fion

4. Person D (Black Widow): Isabella

5. Person E (Hulk): Wayne

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.

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

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

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

For Captain America, Black Widow. USE THIS TEMPLATE TABLE and fill all the blanks

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 =   27 cm Projectile weight = 0.86 grams Stop angle =  55  degree and  72  degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): With an arm length of 27 cm and projectile weight of 0.86 grams, the distance at stop angle 55 degree and 72 degree will have no difference. State the alternative hypothesis (H1): With an arm length of 27 cm and projectile weight of 0.86 grams, the distance at stop angle 55 degree and 72 degree are different.
Step 2: Formulate an analysis plan.	Sample size is 16 which is <30. Therefore t-test will be used. Since the sign of H1 is > , a 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 Run # 2 : Mean: 214.2 cm Standard deviation: 2.96 cm State the mean and standard deviation of Run # 6 : Mean: 191.8 cm Standard deviation: 3.02 cm Compute the value of the test statistic (t):
Step 4: Make a decision based on result	Type of test (check one only) Left-tailed test: [ __ ]  Critical value tα = - ______ Right-tailed test: [✓]  Critical value tα =  1.761 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, and critical value(s), tα or ± tα/2 Since t= 14.01 (> 1.761) Since the test statistics t=14.01 lies in the region of rejection, Therefore Ho is rejected.
Conclusion that answer the initial question	At 0.05 level of significance, it is found that there is a significant change in the flying distance when a different stop angle is being used.
Compare your conclusion with the conclusion from the other team members.	When comparing with the Black Widow (Isabella), we had the same conclusion. Both of us had Ho rejected. Therefore, when the stop angle change, there will be a significant change in the flying distance.
What inferences can you make from these comparisons?	From the comparison made above, I can infer that the stop angle has a significant effect on the flying distance.
Your learning reflection on this Hypothesis testing activity	From this activity, I feel that it is so difficult and confusing for my understanding. Initially, when the lecturer explained the concept to us, I honestly didn’t really understand what is going on and how hypothesis testing works. Firstly, I wasn't really clear on what’s the point of learning this. Secondly, the practice questions were so difficult to understand and lastly, the formulas seems so foreign to me. However, I managed to slowly understand the meaning of doing this hypothesis testing and also with the help of my friend and Dr. Noel’s explanation of the practice question, I could understand more. After all, I’ve learned that hypothesis testing is a step after DOE and it allows me to identify whether a statistical hypothesis is true by studying the entire population. However, It is not possible to get the full accuracy of hypothesis testing because there will be a trade-off involved. But the test can be used to eliminate or accept a hypothesis. However, It will result in an error if one does not eliminate or accept the hypothesis. For the significance level, I feel that this is very important as it can differ with different scenarios. Generally, the larger the significant level, the greater the chance of eliminating the null hypothesis. With that, I feel that overall, hypothesis testing can be very important and useful as it enables us to come up with accurate statistical hypotheses after conducting an experiment and determine if whether the conclusion made after the experiment is valid or invalid. This will probably be useful when I do FYP.