Hypothesis Testing

It is blog time again. 

This time is hypothesis testing. I would be using the full and partial factorial skills i have learn in the DOE lesson. If you want to check it out just go to the DOE page. 

In this page I will be documenting about Hypothesis Testing. 

 It is an ideal way to determine if a statistical hypothesis is true is by examining a sample of a population. Below, I am gonna show you how I apply hypothesis testing on our practical data from our DOE practical

 

 

DOE PRACTICAL TEAM MEMBERS:

1. Person A (Iron Man) - Enzo

2. Person B (Thor) - Jing Hui

3. Person C (Captain America) - Gayathri

4. Person D (Black Widow)- ME 💓💓💓💓💓💓💓💓💓💓💓💓💓💓💓💓💓💓

5. Person E (Hulk) - Redza

 

 

 I am black widow

First up is to show the practical data. 

Since I am Black widow, I am doing runs 4 and 8

The QUESTION	To determine the effect of the 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 =  27.9cm Projectile weight = 2.02grams Stop angle = 60 degree and 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0):  When the arm length is 27.9cm and the projectile weight is 2.02g, the distance traveled by the projectile using a stop angle of 60 degrees and 90 degrees will have no difference  run 4 and 8 have equal distance tranvelled. State the alternative hypothesis (H1): When the arm length is 27.9cm and the projectile weight is 2.02g the distance travelled by the projectile using a stop angle of 60 degrees will be lower than using a stop angle of 90 degrees run 4 will have a shorter distance travelled by the projectile than run 8
Step 2: Formulate an analysis plan.	Sample size is 16 Therefore t-test will be used. 8 runs for run 4, and 8 runs for run 8 Since the sign of H1 is <, a left tailed test is used. Significance level (α) used in this test is 0.5
Step 3: Calculate the test statistic	State the mean and standard deviation of Run # 4: Mean =  149.6 Standard deviation = 1.85 State the mean and standard deviation of Run #8: Mean = 100.1 Standard deviation = 3.00 Compute the value of the test statistic (t): V= 8+8 -2 = 14 a = ((8x1.85^2 + 8x3^2)/ 8+8-2)^(1/2) , a = 2.6643 t = (149.6 - 100.1) / (2.6643 x (1/8 + 1/8)^1/2) t= 37.16
Step 4: Make a decision based on result	Type of test (check one only) Left-tailed test: [ this one ]                                                                                                     Signifiance level = 0.05                                                               Confidence limit = 0.975                                                                     V= 14 Critical value tα = -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 -2.145 > -37.16, -37.16 lies in the negative red zone. SO it is rejected at a significance level of 0.05 Therefore Ho is false.
Conclusion that answer the initial question	When the arm length is 27.9cm and the projectile weight is 2.02g the distance travelled by the projectile using a stop angle of 60 degrees will actually be higher than using a stop angle of 90 degrees. This shows that my hypothesis is wrong
Compare your conclusion with the conclusion from the other team members.	Iron Man: Enzo Thor: Jing Hui The projectile weight really caused a difference between the 2 flying distances.  Hulk: Redza  Using a lighter projectile weight of 0.86g results in a further flying distance of the projectile Using a heavier weight of 2.07g instead of 0.86g will result in a shorter flying distance of the projectile  Captain america: Gayathri She got the same conclusion as me that the stop angle of 60 degrees will cause the projectile to fly further.  Her standard deviation is closer to each other than mine. Hers is 3.42 and 3.18 while on the other hand mine is 1.85 and 3
What inferences can you make from these comparisons?	As the weight of the projectile increases, the flying distance of the projectile decreases As the stop angle increase, the flying distance of the projectile decrease
Your learning reflection on this Hypothesis testing activity	It is quite fun, as it is like limits and it was interesting to see if my values would cross the limits or not.  Overall, I still had to refer to the exercise I did with my class a few weeks ago. But aside from that, it went quite smoothly.  I still remember from my amazing lecturer Mr Chua, the default significance level (a) should be 0.05. This would ensure that it would not skew and mess with our results. If it goes larger, it can be bad.  We also should be honest, and not manipulate or come up with values so that it favours us.  All in all it was a fun activity and I hope to do it again

This blog has been so fun and engaging. 

But all good things must come to an end, so this is the end of my blog on Hypothesis testing. 

My next blog would be up soon 

Pics of Black widow