Blog 5: Hypothesis Testing

Person D (Black Widow: Runs #4 & #8

To determine the effect of stop angle 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 cm

Projectile weight (B) = 2.0117 grams

Stop angle (C) =10 degrees and 40 degrees

State the null hypothesis (H₀):

Using the lower stop angle (Run #4) and the higher stop angle (Run #8) results in the same distance travelled by the projectile.

𝜇₄ = 𝜇₈

State the alternative hypothesis (H₁):

Using the lower stop angle (Run #4) would have a larger distance travelled by the projectile compared to using the higher stop angle (Run #8 ).

𝜇₄ > 𝜇₈

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 #4:

Mean: 75.3 cm

Standard Deviation: 0.93 cm

State the mean and standard deviation of Run #8:

Mean: 40.2 cm

Standard Deviation: 0.79 cm

Compute the value of the test statistic (t):

Type of test (check one only)

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

2.Right-tailed test:[ ✔️ ] Critical value t_α= 1.761

3.Two-tailed test:[ __ ] Critical value t_(α/2)= ± ______

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

Therefore H₀ is false.

Conclusion that answers the initial question: Using a lower stop angle would result in the projectile travelling a further distance after being launched compared to using a higher stop angle.

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

Using Kerri's (Captain America) data as a point of comparison, it can be concluded that H₀ should be rejected. Therefore, H₁ is correct that the stop angle of the catapult has a significant impact on the projectile travelling distance and that a lower stop angle will yield a higher projectile travelling distance than a higher stop angle.

https://cp5070-2022-2b02-group2-kerri.blogspot.com/p/hypothesis-testing.html ^Her blog

What inferences can you make from these comparisons?

Using a lower stop angle will always yield a larger projectile travelling distance and vice versa. This relationship is not affected by changes in the other factors of arm length and projectile weight.

Learning Reflection

Hypothesis testing and DOE were quite difficult for me to pick up initially. When I sat through the CPDD class and listened to Mr Chua teach the lesson, it felt like I was learning another language. But after some self-study, I began to understand what hypothesis testing was and the rationale behind it. During the group challenge of the DOE practical, I realised how hypothesis testing could be put to use. Though with the challenge's small scale, most of the catapult shots could be randomly guessed and there was no real consequence in missing. However, for large engineering projects that have massive stakes and only one attempt, like launching a spacecraft, hypothesis testing is extremely crucial as data can be analysed to calculate the trajectory and other launch factors. Overall, learning hypothesis and statistical skills will benefit me beyond purely engineering.