Hypothesis Testing

 HYPOTHESIS TESTING TASK FOR INDIVIDUAL BLOG

 

For this assignment, you will use the DOE experimental data that your practical team have collected both for FULL Factorial and FRACTIONAL Factorial.

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

1. Darius (Iron Man)

2. Uzair (Thor)

3. Dorson (Captain America)

4. Person D (Black Widow)

5. Person E (Hulk)

6. Person F (Hawkeye)

 

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

 

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

Iron Man will use Run #2 from FRACTIONAL factorial and Run#2 from FULL factorial.

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

Captain America will use Run #5 from FRACTIONAL factorial and Run#5 from FULL factorial.

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

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

Hawkeye will use Run #8 from FRACTIONAL factorial and Run#8 from FULL factorial.

USE THIS TEMPLATE TABLE and fill all the blanks

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 =  32(+) , 26.7(-)cm Start angle = 19(+) 2(-) degree Stop angle = 90(+) 55(-) degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The distance produced by the projectile from Catapult A is the same distance produced by the projectile from Catapult B A=B   State the alternative hypothesis (H1): The distance produced by the projectile from Catapult A is different from the distance produced by the projectile from Catapult B A ≠ 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 5%
Step 3: Calculate the test statistic	State the mean and standard deviation of sample catapult A: Mean: 100.8, standard deviation: 10.20     State the mean and standard deviation of sample catapult B: Mean: 89.6 standard deviation:4.47     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: [ _tick_ ]  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 Ttest  falls outside the range of -2.145 to +2.145 Therefore Ho is rejected.
Conclusion that answer the initial question	Ho is rejected hence catapult A does not produce the same projectile distance as catapult B.
Compare your conclusion with the conclusion from the other team members.   What inferences can you make from these comparisons?	Darius: Accept Ho, reject H1 with significance level of 5% Dorson: Reject Ho, accept H1 with significance level of 5% Uzair: Reject Ho, accept H1 with significance level of  5% For Darius' conclusion, he is able to accept his Ho as his mean values for both fractional and full factorial are similar, therefore, the t value would fall within this tα range. Making his Ho acceptable. For Dorson's case, his case is similar to mine in a sense that the difference between our mean values is very significant. therefore making the t value large, not falling between the tα range.  inference for significant level of 5% The standard deviation for my case is rather large and also the difference between the standard deviation between fractional and full factorial is very significant from 10.20 to 4.47. This may be due to uncontrollable factors. One uncontrollable factor is the human error. We can only measure the distance the projectile has travelled using a measuring tape. Different people were taking measurements and therefore the strategy for measuring the distance is also compromised as different people have different strategies. Another reason is due to the starting point of the catapult. Again, there might be different people handling the catapult and the starting point distance might vary depending on persons as different people have different principles of measurements. Therefore, this might affect the measured distance travelled and hence the mean and standard deviation of the design of experiments.

 REFLECTION:

Going into the lesson, I felt inferior to the people who took statistics as an elective. Nevertheless they are still my friends and I can go to them for help. The formulas were alien to me as I saw different symbols and letters representing different things. But as I got to know more about the topic, it became easier for me to understand as I got used to it by doing the different calculation questions. It is not easy, but at the same time, it is not difficult. It just takes abit of time to recall the formulas and apply it. Having said that, it took me awhile for me to understand what was going on. I was confused as to what was happening and what were the formulas representing, but after consulting my groupmate, Zhi Wei, that takes statistics as an elective, she explained to me about the formulas and the strategies that were used into tackling the questions. I got more confident as I understood them and got excited when I actually solved a question on my own.