Hypothesis Testing

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What is Hypothesis Testing?

Hypothesis testing is procedure meant to test out an assumption made about a population parameter. Tested hypotheses may or may not be rejected based on the results obtained from testing for different factors as mentioned in the previous blog.

Hypothesis testing usually makes use of samples. Samples are a portion of a population. Ideally, information about the entire population should be used but usually, impractical, random samples are taken from the population instead

For this assignment, I will use the DOE experimental data using the CATAPULT experiment that my group had conducted during the practical. I will use FULL FACTORIAL DATA.

DOE PRACTICAL TEAM MEMBERS (fill this according to your DOE practical):

1. Reinard (Iron Man)

2. Clive (Thor)

3. Adyl (Hulk)

4. Joelle (Black Widow)

The QUESTION

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 = __28__cm

Projectile weight = __0.89___ grams and ___2.01___ grams

Stop angle = __120___ degree

Step 1:

State the statistical Hypotheses

State the null hypothesis (H0):

Projectile weight has NO SIGNIFICANT EFFECT on flying distance of the projectile

State the alternative hypothesis (H1):

Projectile weight HAS SIGNIFICANT EFFECT on flying distance of the projectile

H0 ≠ H1

Step 2:

Formulate an analysis plan.

Sample size is _8__ Therefore t-test will be used.

Since the sign of H1 is _≠_, a two-tailed test is used.

Significance level (α) used in this test is _0.05_

Step 3:

Calculate the test statistic

State the mean and standard deviation of Run # 6:

mean: 185.0cm

Standard Deviation: 5.68

State the mean and standard deviation of Run #8:

Mean: 173.8cm

Standard Deviation: 2.85

Compute the value of the test statistic (t):

v= 8+8-2 = 14

Step 4:

Make a decision based on result

Type of test (tick one only)

Left-tailed test: [ __ ] Critical value tα = - ______
Right-tailed test: [ __ ] Critical value tα = ______
Two-tailed test: [ ] Critical value tα/2 = ± 2.145

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

Therefore Ho is rejected.

Conclusion that answer the initial question

Based on the hypothesis testing, and the two-tailed diagram result, the projectile weight does have a significant effect on the flying distance

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

Comparing my results with Thor and Iron Man, we have reached a consensus whereby the heavier the weight, the shorter the flying distance. However, due to some outliers and incorrect data collected during the experimental phase, both Thor and Iron man derived a type ii error accepted null hypothesis. But upon further discussion, they realized that the Null hypothesis should be rejected. Hence, the Projectile weight has a significant effect on the flying distance. However, Blackwidow has yet to come up with her findings but I will update this blog as soon as I have the information. This goes to show that sometimes, in random samples or even tiny mistakes in the experimental phase, small mistakes can cause a huge discrepancy in the predicted result.

Your learning reflection on this Hypothesis testing activity

Overall I enjoyed this Hypothesis Testing activity as it dug deeper into analyzing experimental data and actually learning how to make sense of them. After conducting the experiment and doing the calculations, it is clear to me why samples of a population are taken instead of the entirety of a population - there would just be too much data to comprehend, and taking random samples would be more efficient for roughly the same conclusion.