Hypothesis Testing

Hypothesis Testing Task

Person A (Iron Man)

Run #1 and Run#3 will be utilized 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, the different users will not have any effect on the flying distance of the projectile.

Flying distance for the catapult is collected using the factors below:

Arm length (A) = ____cm

Projectile weight (B) = _____ grams and ______ grams

Stop angle (C) = _____ degree

1. State the statistical hypothesis

State the null hypothesis (H₀):

Null Hypothesis:

Using the lighter projectile (Run #1) and the heavier projectile (Run #3) will result in the same distance traveled by the projectile.

𝜇₁ = 𝜇₃

State the alternative hypothesis (H₁):

Alternative Hypothesis:

Using the lighter projectile (Run #1) will result in a larger distance traveled by the projectile compared to using the heavier projectile (Run #3 ).

𝜇₁ > 𝜇₃

2. Formulate an analysis plan

The sample size is 16 as there are 2 runs of 8, therefore T-test will be used.

Since the sign of H1 is >, a right-tailed test is used.

The significance level (α) used in this test is 0.05

3. Calculate the test statistic

State the mean and standard deviation of Run #1:

Mean: 254.8 cm

Standard Deviation: 14.20 cm

State the mean and standard deviation of Run #3:

Mean: 235.9 cm

Standard Deviation: 4.81cm

Compute the value of the test statistic (t):

4. Make a decision based on the result 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 = ± ______

Use the t-distribution table to determine the critical value of tα or tα/2

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

Since the critical value of t when there is a distribution of 95%, v=14 is 1.761. T is in the rejection region and therefore H₀ is rejected as it lies in the region of rejection.

I conclude that the use of a lighter projectile would result in a larger flying distance of the projectile while using a heavier projectile would result in a shorter distance flown.

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

Comparing my team members conclusions with my own, I find that the projectile weight and stop angle have an effect on the distance traveled by the projectile. This is because in both members findings had H0 rejected and H1 accepted. While the other 2 had the same finding s of H0 rejected and H1 accepeted, resulting in the stop angle having an effect on the distance traveled by the projectile.

What inferences can you make from these comparisons?

I can infer that it is certain that the use of a lighter projectile would result in a larger flying distance of the projectile and the smaller the stop angle the larger the flying distance of the projectile.

Learning Reflection:

When first introduced to Hypothesis Testing, I was very taken aback by the sheer amount of content that was withheld in this chapter. I felt that there were many new letters to take note of and many new terms to understand and implement. I did not understand how anything worked until I had to apply it to the practice questions, that was where I learned how to carry out the whole hypothesis testing equations. However, now that I am easily able to carry out hypthesis testing and apply it in my learning it can be used when I need to examine my data to provide accurate conclusions about my hypothesis. I know this skill will be important and helpful when I have my FYP and Capstone project.