What is hypothesis testing? It is to check if the assumption of the population parameter is true or not. Hypothesis testing is a statistical method used to make inferences about a population based on a sample of data. It involves formulating a null hypothesis and an alternative hypothesis, and then using statistical techniques to determine which hypothesis is more supported by the data.
This is the data that my group obtained from the DOE practical. I will be Person E (Hulk). I will using Run#6 and Run#8.
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 (A) = ____cm
Projectile weight (B) = _____ grams and ______ grams
Stop angle (C) = _____ degree
State the null hypothesis (H₀):
Using the smaller projectile weight (Run #6) and the larger projectile weight (Run #8) results in the same distance travelled by the projectile.
𝜇6 = 𝜇8
State the alternative hypothesis (H₁):
Using the smaller projectile weight (Run #6) would have a further distance travelled by the projectile compared to using the larger projectile weight (Run #8).
𝜇6> 𝜇8
Sample size is 16. Therefore t-test will be used.
Since the sign 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#6
Mean: 87.2 cm
Standard Deviation: 0.96 cm
State the mean and standard deviation of Run#8
Mean: 81.6 cm
Standard Deviation: 0.98 cm
Compute the value of the test statistic (t):
Type of test
1.Left-tailed test: [ __ ] Critical value tα= - ______
2.Right-tailed test:[ ✔️ ] Critical value tα= 1.761
3.Two-tailed test:[ __ ] Critical value tα/2= ± ______
Since t>tα, H₀ is rejected
Hence, H₀ is false.
Conclusion that answer the initial question
Using a lighter projectile will result in a larger flying distance of the projectile compared to using a heavier projectile
Compare your conclusion with the conclusion from the other team members
Black Widow [Matthias] - Using a lighter projectile leads to the projectile flying a larger distance while using a heavier projectile leads to the projectile flying a shorter distance.
Captain America [Eng Kiat] -
Thor [Sreenithi] - Using a smaller stop angle is used, the projectile will travel a greater distance. However when a larger stop angle is used, the projectile will travel a shorter distance
Iron Man [Abhishek] - the larger the stop angle the further the ball travels and the smaller the stop angle the lesser the ball travels
Hulk [Me] - Using a lighter projectile will result in a larger flying distance of the projectile compared to using a heavier projectile
Inference from these Comparisons
Comparing with all the conclusion, we can infer that using a LOW(-) value will increase the projectile travel distance. Therefore, if we want the projectile to travel far, it is recommended to use the LOW(-) values. This can be seen from Run#1 where all are LOW(-) values and has the largest projectile travel distance.
Learning Reflection
When Mr Chua first introduce Hypothesis testing to us, I was very confused about what it really was. Personally, I am not very good with statistics, hence, I was very scared and hesitant to learn more about it. However, when Mr Chua assigned us some practices, I was able to understand it more and as I was slowly getting the hang of what it was really about. I come to appreciate the importance of Hypothesis Testing.
Hypothesis Testing is a powerful tool for making decisions and drawing conclusions about populations based on limited data. This is especially important in scientific research, where it is often not feasible to collect data on the entire population of interest.
In addition, I found that clearly defining the null and alternative hypotheses is important. The null hypothesis represents the default assumption, while the alternative hypothesis represents the opposite assumption. It is important to choose hypotheses that are well-defined, clear, and relevant to the research question.
During the lesson, Mr Chua also shared with us the importance of integrity when handling with statistical data. I felt that this was very important, especially medical data where the limit has to be more stringent for the safety of patients and manipulating it towards our favor is unethical and dangerous.
In conclusion, hypothesis testing is a powerful tool for making inferences about populations based on a sample of data. I have come to appreciate the importance of the uses of hypothesis testing to help us with our experiments.
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