Hypothesis Testing
Hey guys welcome back to my blog again this will be one of the last blogs I'll be posting as this semster is coming to end soon ππ.
For this practical our groupmates are split into 5 different characters and each of us unique characters will need to perform hypothesis testing on our respective runs
- Jiatong [Iron Man]: Runs #1 and #3
- Devin [Thor]: Runs #2 and #4
- Junkai [Captain America]: Runs #2 and #6
- Aminur [Black Widow]: Runs #4 and #8
- Jihinn [Hulk]: Runs #6 and #8
Data collected for FULL factorial deisgn use CATATPUT (fill this according to your DOE practical result):
The Question/Aim: 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. there different user will not have any effect on the flying distance of projectile.
Flying distance for catapult is collected using the factors below:
Arm length = 33 cm
Projectile weight = 2.08 grams
Stop angle = 30 degree and 50 degree
State the statistical hypotheses
State the null hypothesis (H₀):
When arm length is at 33cm and projectile weight is at 2.08 grams, the flying distance of the projectile using a stop angle of 30 degree and 50 degree will have no difference.
Β΅₂ = Β΅₆
State the alternative hypothesis (H₁):
When arm length is at 33cm and projectile weight is at 2.08 grams, the flying distance of the projectile using a stop angle of 30 degree and 50 degree will are different.
Β΅₂ < Β΅₆
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 (Ξ±) used in this test is 0.05
Calulate the test statistic
0)State the mean and standard deviation of Run #2:
Mean: 149.25 cm
Standard Deviation: 4.10 cm
State the mean and standard deviation of Run #6:
Mean: 196 cm
Standard Deviation: 4.11 cm
Compute the value of test statistic:
Make a decision based on result
Type of test (check one only)
1. Left-tailed test: [✅] Critical value ta = - 1.761
2. Right-tailed test: [__] Critical value ta = __.
3. Two-tailed test: [__] Critical value ta/2 = ± __.
At CL = 0.95, the percentile is the 95th percentile. Therefore, at v = 14 , t0.95 = -1.761
Since the t = -21.306 which is inside the rejection region, the null hypothesis (H₀) is rejected.
Therefore, H₀ is false.
Conclusion that answer the inital question
Using a bigger stop angle would result in a larger flying dsitance of the projectile while using a smaller stop angle would result in a smaller flying distance of the projectile.
Compare your conclusion with the conclusion from the other team members.
Iron Man [Jia Tong]: When the projectile weight is lighter, the flying distance will be longer.
Thor [Devin]: Using a lighter Projectile Weight of 0.88grams will result in a further flying distance travelled by the projectile.
Captain America [Jun Kai]: Using a bigger stop angle would result in a larger flying distance of the projectile while using a smaller stop angle would result in a smaller flying distance of the projectile.
Black Widow [Aminur]: When the arm length is 33 cm and the projectile weight is 2.08 grams, the distance travelled by the projectile using a stop angle of 30 degrees is lower than using a stop angle of 50 degrees.
Hulk [Ji Hinn]: When the arm length and stop angle of the catapult remain constant at 33 cm and 50 degrees respectively, as the projectile weight decreases from 2.07g to 0.88g the distance travelled increases.
What inferences can you make from these comaparisons?
I can infer that as the weight of the projectile decreases, the flying distance of our projectile increases.
I can also infer that as the stop angle increases, the flying distance of our projectile also increases.
Your learning reflection on this Hypothesis testing acitivity
After attending the lecture by Mr Chua my CPDD teacher, I have learnt so much about hypothesis testing and also realised that there were more aspects of testing than I've expected. I thought that just by looking at the raw data we could already tell if the hypothesis valid however I was wrong.
There were steps we had to follow for instance specifying a null hypothesis and and an alternative hypothesis, calculating a test statistic and making a decision bsaed on the level of significance and v-value.
The process of hypothesis testing activity was more tedious that I've expected and when I was completing the prepractical activity I had took a long time to complete each question. However, in the end I was able to master it and i think i would be able to apply it in the future when i need to test out performance of my chemical device.
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