Blog 5 (Hypothesis Testing)

Hello everyone! Welcome back to my blog! This time I will be sharing my experience with hypothesis testing.

Person C (Captain America): Run #2 and #6

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) = 33 cm

Projectile weight (B) = 0.86 grams

Stop angle (C) = 55 degree and 90 degree

State the null hypothesis (H₀):

Using the smaller stop angle (Run #2) and the larger stop angle (Run #6) results in the same distance travelled by the projectile.

𝜇2 = 𝜇6

State the alternative hypothesis (H₁):

Using the smaller stop angle (Run #2) would have a longer distance travelled by the projectile compared to using the larger stop angle (Run #6).

𝜇2 > 𝜇6

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: 175.0 cm

Standard Deviation: 3.32 cm

State the mean and standard deviation of Run #6:

Mean: 103.0 cm

Standard Deviation: 2.29 cm

Compute the value of the test statistic (t):

Type of test (check one only)

Right-tailed test: [ ✔️ ] Critical value tα= 1.761

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

Therefore Ho is false.

Conclusion that answers the initial question:

Using a smaller stop angle would result in a longer flying distance of the projectile while using a larger stop angle would result in a shorter flying distance.

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

Vietnam soldier (Iron Man): Using a lighter projectile weight would result in a larger flying distance of the projectile while using a heavier projectile weight would result in a shorter flying distance.

Jeremy Tan (Thor): Using a lighter projectile weight would result in a larger flying distance of the projectile while using a heavier projectile weight would result in a shorter flying distance.

Yan Zhen (Captain America): Using a smaller stop angle would result in a larger flying distance of the projectile while using a bigger stop angle would result in a shorter flying distance.

Muruguru (Black Widow): Using a smaller stop angle would result in a larger flying distance of the projectile while using a bigger stop angle would result in a shorter flying distance.

What inferences can you make from these comparisons?

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

• Using a smaller stop angle would result in a larger flying distance of the projectile while using a bigger stop angle would result in a shorter flying distance.

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Learning Reflection

From the lesson on Hypothesis Testing, we learnt that a statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. To determine their validity, we need to carry out Hypothesis Testing. This involves formal procedures used by experimenters or researchers to accept or reject statistical hypotheses. We were introduced to the steps in Hypothesis Testing. Admittedly, it was very confusing when formulating an analysis plan. From an experiment, we had to decide whether the statistical test is a one-tailed or two-tailed test by determining the sign of alternative hypothesis. Afterwards, we had to calculate the test statistic by using a formula. To decide whether we accept or reject the null hypothesis is by means of defining an acceptance region. To allow us to familiarize with the steps, our lecturer gave us some practice questions and it had really helped me deepened my understanding on hypothesis testing. With my newly attained knowledge, I was able to complete the Hypothesis Testing task above. Overall, I was able to understood the significance of hypothesis testing in the outside world. Ideally, it would be best if we could determine the validity of the hypothesis by examining the entire population of the world. However, it is clearly impractical. Thus, a random sample is selected from the population for examination. The sample has to be reliable to ensure that the results are genuine. I hope that I will be able to successfully use hypothesis testing in my upcoming projects.