Hypothesis Testing

What's up guys!!! Today I will be bringing you on a journey with me to experience this Hypothesis Testing!😀😀😀

For this assignment, I will use the DOE experimental data using the CATAPULT that my group and I have conducted during the practical. I will be using FULL FACTORIAL DATA.

My team members' allocated roles:

• Me: Thor 🔨🗲 (Run #2 and Run #4)
• Jianye: Black Widow 💣❤ (Run #4 and Run #8)
• Yu Han: Iron Man 💥🔥 (Run #2 and Run #3)
• Brice: Captain America 🚩💪 (Run #2 and Run #6)
• Jian Lun: Hulk 💪(Run #3 and Run #8)

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

I will be using Run #2 and Run#4 to determine the effect of projectile weight.

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 is collected using the factors below: Arm length = 33.1 cm Projectile weight = 0.86 grams and 2.87 grams Stop angle = 70 degree

Step 1: State the statistical hypotheses

State the null hypothesis (H0): When the Arm Length is 33.1cm and the Stop Angle is 70 degrees, the flying distance travelled by the projectile using Projectile Weights of 0.86g and 2.87g will be the same. State the alternative hypothesis (H1): When the Arm Length is 33.1cm and the Stop Angle is 70 degrees, the flying distance travelled by the projectile using Projectile Weight of 0.86g will be further than the flying distance travelled by the projectile using Projectile Weight of 2.87g.

Step 2: Formulate an analysis plan

Sample size is 16. Therefore t-test will be used. Since the sigh of H1 is >, 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 of Run #2 = 145.3cm Standard Deviation of Run #2 = 4.43cm State the mean and standard deviation of Run #4: Mean of Run #4 = 140.3cm Standard Deviation of Run #4 = 3.33cm 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 =  1.761 3. Two-tailed test: [ _ ] Critical value tα/2 = ± ____ Compare the values of test statistic (t) and critical values (tα): Using the diagram, for right-tail test, since t = 2.39 is greater than tα = 1.761, it lies in the rejection range. Therefore, H0 is rejected.

Conclusion that answer the initial question

• Using a lighter Projectile Weight of 0.86g will result in a greater flying distance travelled by the projectile when Stop Angle and Arms Length remains the same.
• Using a heavier Projectile Weight of 2.07g will result in a shorter flying distance travelled by the projectile when Stop Angle and Arms Length remains the same.

Compare your conclusion with the conclusions from other team members

• Me: Thor 🔨🗲 (Run #2 and Run #4)
• Jianye: Black Widow 💣❤ (Run #4 and Run #8)
• Yu Han: Iron Man 💥🔥 (Run #2 and Run #3)
• Brice: Captain America 🚩 (Run #2 and Run #6)
• Jian Lun: Hulk 💪(Run #3 and Run #8)

Black Widow's conclusion: Click here to view Black Widow's blog

The distance travelled by the projectile reduces when the Stop Angle increases from 50 to 70 degrees while the Arms Length and the Projectile Weight remain unchanged.

Iron Man's conclusion: Click here to view Iron Man's blog

The distance travelled by the projectile will decrease when the Projectile Weight is increased (from 0.86g to 2.87g), while the Arms Length and Projectile Weight remains constant.

Captain America's conclusion: Click here to view Captain America's blog

This indicates that the distance travelled by the projectile reduces when the Stop Angle increases from 50 degrees to 70 degrees while the Arm Length and Projectile Weight are constant.

Hulk's conclusion: Click here to view Hulk's EMPTY blog

Sadly, Hulk did not do his blog 😭😭

What inferences can I make from these comparisions?

1. The distance travelled by the projectile will indeed decrease when the Projectile Weight is increased from 0.86g to 2.87g, while Arm Length and Stop Angle remains the same.
2. The distance travelled by the projectile will decrease when the Stop Angle is increased from 50 degrees to 70 degrees, while the Arm Length and Projectile Weight remains the same.

My learning reflection on this Hypothesis Testing activity

Through the lessons and acivities of Hypothesis Testing I have learned a lot things. First of all, I learned the difference between a statistical hypothesis and a hypothesis testing. A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. While, hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses. I also learned the steps in Hypothesis Testing and how to apply them. They can be seen in the diagram below.

Additionally, with the help of Hypothesis Testing, I leanred how the different factors (arms length, projectile weight & stop angle) affects the distance travelled by the projectile. In the future, I will apply what I learned and use Hypothesis Testing to justify my conclusion.