Blog 4

Hi everyone, today I will be documenting about hypothesis testing. I will be using the DOE experimental full factorial data from the catapult practical. So what exactly is hypothesis testing? Firstly lets talk about statistical hypothesis....A statistical hypothesis is an assumption about a population parameter. The

assumption may or may not be true. Hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.

In this blog, I will be taking the role of Thor and walk you through using Run#2 and Run#4. To determine the effect of projectile weight.

These are my group members and their hero, if you are interested and want to learn hypothesis testing from their runs you make click on their blogs

Jing Yue (Iron Man)

Iron Man will use Run #1 and Run#3. To determine the effect of projectile weight

Jing Yue Blog

Mabelle (Captain America)

Captain America will use Run #2 and Run#6. To determine the effect of stop angle

Mabelle Blog

Dhasna (Black Widow)

Black Widow will use Run #4 and Run#8. To determine the effect of stop angle

Here is my data from the catapult experiment:

The QUESTION	To determine the effect of Projectile Weight on the flying distance of the projectile
Scope of the test	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 = 0.86 grams and 2.07 grams Stop Angle = 45 degrees
Step 1: State the statistical Hypotheses	State the null hypothesis (H0): When the Arm Length is 33cm and the Stop Angle is 45 degrees, the flying distance travelled by the projectile using a Projectile Weight of 0.86grams 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 45 degrees, the flying distance travelled by the projectile using a Projectile Weight of 0.86grams will be further than the flying distance travelled by the projectile using a Projectile Weight of 2.07grams. 𝜇2 > 𝜇4
Step 2: Formulate an analysis plan	Sample size is 8. 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.
Step 3: Calculate the test statistic	State the mean and standard deviation of Run#2 mean-94.3cm, standard deviation-2.87cm State the mean and standard deviation of Run#4 mean 83.5cm, standard deviation-3.32cm 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: [ X ]  Critical value tα = 1.943 3. Two-tailed test: [ ]  Critical value tα/2 = ± ____ 3.56 > 1.943. Therefore Ho is rejected at 0.05 level of significance
Conclusion that answer the initial question	using the lighter the projectile weight of 0.86grams will result in a further distance travelled. On the other hand, using a heavier projectile weight of 2.07grams will result in a shorter distance travelled
Compare your conclusion with the conclusion from the other team members.	JingYue (Iron Man): at 28cm arm length and 45˚ stop angle, the flying distance of the projectile using 0.86g projectile weight and 2.08g projectile weight are different. Thus, projectile weight effects the flying distance of the projectile. Mabelle (Captain America): stop angle does not have a significant effect on flying distance of projectile. Dhasna (Black Widow): we can conclude that at 33cm arm length and a projectile weight of 2.08 grams, the flying distance of the projectile does not differ when using either 90 degrees stop angle or 45 degrees stop angle . Thus, stop angle does not affect the flying distance of the projectile.
What inferences can you make from these comparisons?	comparing Jinyue and my conclusion, using a lighter weight projectile will result in a further distance travelled comparing Mabelle and Dhasna conclusion, changing the stop angle does not affect the flying distance of the projectile significantly.

Reflection

Through my recent experience with hypothesis testing, I've learned its importance in drawing conclusions from samples when examining larger populations. Since it's impractical to study entire populations, hypothesis testing provides a practical way to make educated guesses based on smaller samples.

However, I've also realized that hypothesis testing isn't foolproof. If the samples don't accurately represent the population, we might make mistakes in our conclusions. I find that hypothesis testing is slightly troublesome as It involves a fair amount of data collection and calculations, like figuring out test statistics and standard deviations. Luckily, tools like Excel can help with these tasks, especially if we already have mean and standard deviation values.

One big lesson I've learned is about the level of significance. This is crucial because it ensures the reliability of our conclusions. Mr. Chua shared a story about a group changing their significance level to match their desired outcome, which made their results unreliable and cost them marks. This taught me the importance of honesty and sticking to the proper methods in statistical analysis. Moving forward, I'm committed to maintaining integrity in my projects and avoiding the temptation to manipulate results or significance levels to fit what I want to see.

That is all for this blog on hypothesis testing, I hope you can appreciate the use of hypothesis testing and be able to apply it in your future. Thankyou for your time and hope to see you in the next blog!