Blog 5: Hypothesis Testing

Hypothesis Testing Task

Person A (Iron Man): Run #1 and #3

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) = 28 / 33 cm

Projectile weight (B) = 0.8619 grams and 2.0117 grams

Stop angle (C) = 10 / 40 degrees

State the null hypothesis (H₀):

Using the lighter projectile (Run #1) and the heavier projectile (Run #3) results in the same distance travelled by the projectile.

𝜇₁ = 𝜇₃

State the alternative hypothesis (H₁):

Using the lighter projectile (Run #1) would have a larger distance travelled by the projectile compared to using the heavier projectile (Run #3 ).

𝜇₁ > 𝜇₃

Sample size is 16 Therefore t-test will be used.

Since the sign of H1 is > , a ̶l̶e̶f̶t̶/̶t̶w̶o̶/right tailed test is used.

Significance level (α) used in this test is 0.05

State the mean and standard deviation of Run #1:

Mean: 113.5 cm

Standard Deviation: 1.49 cm

State the mean and standard deviation of Run #3:

Mean: 101.4 cm

Standard Deviation: 1.36 cm

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

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

Compare the values of test statistics, t, and critical value(s),tα or ±̶t̶α̶/̶2̶

Therefore Ho is false.

Conclusion that answers the initial question:

Using a lighter projectile would result in a larger flying distance of the projectile while using a heavier projectile would result in a smaller flying distance.

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

Both Thor and Hulk came to the same conclusion with mine that the weight of the projectile would have a significant impact on flying distance and that using a lighter projectile results in a larger flying distance.

What inferences can you make from these comparisons? Using a lighter projectile will always result in a larger flying distance and vice versa. This relationship is not affected by changes in the other factors of arm length and stop angle.

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Learning Reflection

During the CPDD physical lesson, I initially did not understand how to do the math behind hypothesis testing. I had not learnt anything about hypothesis testing before so this was something new. The slides defining type 1 and type 2 errors confused me at first as I didn't know what a null hypothesis was. I also was unfamiliar with the steps behind hypothesis testing. After our lecturer, Mr. Chua, went through the slides with the class, I looked through the slides at my own pace but I was still unsure. After trying out the practice questions myself, I slowly got familiar and understood the steps. For the first question, Mr. Chua showed us the steps so we could look through it on our own and understand the methods better. From question 1, I did not understand why the percentile increased from the confidence limit. After talking to my friend who asked Mr. Chua already, I learned that it was from taking the significance and dividing it by 2 and adding it to the confidence limit because the test was 2-tailed. After that, I was able to do the rest of the practice questions on my own to increase my familiarity with the steps. This helped me out when I did the hypothesis testing task. I am not sure when I will use the hypothesis testing method in the future, probably during the final year project (FYP), but I will try to implement what I have learnt in the future.