Blog 5 (Hypothesis Testing)

Hello Everyone😺😺Welcome to this week's blog. For this blog, I will be documenting about Hypothesis Testing😱 You all may ask what is Hypothesis Testing. Well, Hypothesis Testing is an assumption about a population parameter. This assumption may or may not be true. Therefore, we have to carry out experiments to check that whether we can accept or reject the statistical hypotheses. An example of Hypothesis Testing will be documented below.

For this blog, I will be Person B (Thor).
Thor will use Run #2 and Run#4. 

Objective: To determine the effect of projectile weight.

To determine the effect of Projectile Weight 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 is collected using the factors below:

Arm Length =  33 cm

Projectile Weight = 0.88 grams and 2.07 grams

Stop Angle = 30 degrees

State the null hypothesis (H0):

• When the Arm Length is 33cm and the Stop Angle is 30 degrees, the flying distance travelled by the projectile using a Projectile Weight of 0.88grams and 2.07grams will be the same.
• 𝜇2 = 𝜇4

State the alternative hypothesis (H1):

• When the Arm Length is 33cm and the Stop Angle is 30 degrees, the flying distance travelled by the projectile using a Projectile Weight of 0.88grams will be further than the flying distance travelled by the projectile using a Projectile Weight of 2.07grams.
• 𝜇2 > 𝜇4

Sample size is 16. 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.

State the mean and standard deviation of Run #2:

• Mean of Run #2 = 149.25cm
• Standard Deviation of Run #2 = 4.10cm

State the mean and standard deviation of Run #4:

• Mean of Run #4 = 132.38cm
• Standard Deviation of Run #4 = 5.60cm

Compute the value of the test statistic (t):

Type of test (check one only)

1. Left-tailed test: [ __ ]  Critical value tα = - ______

2. Right-tailed test: [ ✔️ ]  Critical value tα =  1.761 (can be found in Topic9-3-t Distribution Table)

3. Two-tailed test: [ __ ]  Critical value tα/2 = ± ______

 

Compare the values of test statistics, t, and critical value(s), tα 

Using the diagram shown above, for right-tail test, since t = 6.43 > tα = 1.761, it lies in the rejection range. Therefore Ho is rejected.

Conclusion that answer the initial question

• Using a lighter Projectile Weight of 0.88grams will result in a further flying distance travelled by the projectile.
• Like wise, using a heavier Projectile Weight of 2.07grams will result in a shorter flying distance travelled by the projectile.

Compare your conclusion with the conclusion from the other team members.

My fellow team members are:

1. 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.
2. 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.
3. 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.
4. Iron Man [Jia Tong]: When the projectile weight is lighter, the flying distance will be longer.

The link to their blog is shown below if you wanna take a look at their results as well👇👇👇

Aminur: Abdul Vivan Bala Young Dicky's Hypothesis Testing

Jun Kai: Jun Kai's Hypothesis Testing

Jia Tong: Jia Tong's Hypothesis Testing

Ji Hinn: Ji Hinn's Hypothesis Testing

What inferences can you make from these comparisons?

From Thor, Iron Man and Hulk conclusion:

• Using a bigger stop angle will result in a further flying distance travelled by the projectile.

From Captain America and Black Widow conclusion:

• Using a lighter projectile weight will result in a further flying distance travelled by the projectile.

Your learning reflection on this Hypothesis Testing activity

From the lecture gone through by Mr Chua, I have learnt so many things about hypothesis testing. For example, the ideal way to determine whether the statistical hypothesis is true by examining the entire population. However, that is not possible as there is a uncountable amount of population. Therefore, researchers will only gather a random sample from the population to test for result. This is a similar process to design of experiment (DOE) where I have learnt a few weeks ago! However, in hypothesis testing, we need to obtain many data such as σ, s, X̅ and t which may be quite a hassle to find as the equation for some of the symbol are quite long. Only after obtaining those values, we then compare whether the hypothesis is true or false using a right/left/two tailed test based on our alternative and null hypothesis. From the lesson, I also learnt that the most common level of α is 0.05 as it is a universal value that most people use and therefore I have chosen it to be 0.05 earlier in the blog. We only use α = 0.01 if we want to tighten the test such as in the case of health science or hospital cases. In conclusion, I had a fun time in lecture as I am able to learn new things and now I got the choice to use Design of Experiment or Hypothesis Testing to obtain a conclusion. In addition, this skills will come in handy in the future when I am working in a lab or plant.