Hypothesis testing

HYPOTHESIS TESTING TASK FOR INDIVIDUAL BLOG

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

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

1. Cheryl (Iron Man)

2. Hong Yi (Thor)

3. Kieron (Captain America)

4. Ruba (Black Widow)


Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result): 

Iron Man will use Run #1 and Run#3. To determine the effect of projectile weight.

Thor will use will use Run #2 and Run#4. To determine the effect of projectile weight.

Captain America will use Run #2 and Run#6. To determine the effect of stop angle.

Black Widow will use Run #4 and Run#8. To determine the effect of stop angle.

 

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 =  33 cm

Projectile weight = 0.85 grams and 2.06 grams

Stop angle = 49 degree

 

Step 1:

State the statistical Hypotheses:

State the null hypothesis (H0): With an arm length of 33 cm and stop angle of 49 degrees, the flying distance of projectile using 0.85 grams projectile weight and 2.06 grams projectile weight will have no difference. 

State the alternative hypothesis (H1): With an arm length of 33 cm and stop angle of 49 degrees, the use of a lighter projectile with a weight of 0.85 grams as compared to 2.06 grams projectile weight will improve the flying distance. 

Step 2:

Formulate an analysis plan.

Sample size is 16 which is lesser than 30. 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

Step 3:

Calculate the test statistic

State the mean and standard deviation of Run # 2:

Mean- 122.9 cm

Standard Deviation- 2.32 cm


State the mean and standard deviation of Run # 4:

Mean- 99.0 cm

Standard Deviation- 1.89 cm

 

Compute the value of the test statistic (t):



 

Step 4:

Make a decision based on 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

 

t=21.132  >  tα=1.761

 

The test statistics t=21.132 lies in the region of rejection.

 

Therefore Ho is rejected.

 

Conclusion that answer the initial question

At 0.05 level of significance, it is found that there is significant improvement in the flying distance of the projectile when a lighter projectile is used.

 

 

 

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

 

Both of us have similar conclusions, a change in projectile weight results in significant change in flying distance.

In addition, from my conclusion, I can also tell that the change in flying distance of the projectile is positive (increase) when the projectile weight is lower.

What inferences can you make from these comparisons?

 

I can infer that there is little interaction between factor A (arm length) and B (projectile weight). The flying distance still increases with a lower projectile weight regardless of whether factor A is high or low.

Your learning reflection on this Hypothesis testing activity

 

Hypothesis testing is a new concept to me and it was very confusing😖 at the start. In the beginning, I was not used to the various symbols for representing the statistical terms. I gradually got used to it after doing the practice questions. While doing the practice question, I had a question in mind which is how do we choose between a one-tailed and two-tailed test. Through the practice question, I learnt that a one-tailed test is used when the change/difference is specified (e.g. significant improvement.

 

Hypothesis testing is the next step after DOE. From DOE, we can analyse the results and find out which factor has the most effect. From there, we can do hypothesis testing and use a suitable test to reject or accept the null hypothesis. We can then come to a conclusion and decide if we should make changes to the factor to achieve the desired outcome.

 

Something important in hypothesis testing is the significance level. From the lesson, I learnt that different scenarios use different values of significance level. If the consequence of committing type I error is severe, a more stringent significance level is used.

 

Hypothesis testing is a very useful tool to use together with DOE. I can apply what I have learnt in my FYP. After applying the DOE, I can make use of hypothesis testing to determine if my conclusion is valid and make use of the results to further my design for the capstone project.