Hypothesis Testing

 

HYPOTHESIS TESTING TASK FOR INDIVIDUAL BLOG

For this assignment, you will use the DOE experimental data using the CATAPULT that you have conducted during the practical. You will use FULL FACTORIAL DATA. You are free to express yourself in your blog, but the table provided on page 2 to 7 must be followed.

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

1. Hannah (Iron Man)

2. Justin (Thor)

3. En Ting (Captain America)

4. Jun Hao (Black Widow)

5. Keith (Hulk)

 

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.

Hulk will use Run #6 and Run#8. To determine the effect of projectile weight

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 =  12.5 cm Projectile weight = 0.86 grams and 2.05 grams Stop angle = 49 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): At 12.5cm arm length and 49 degree stop angle, the flying distance of the projectile using 0.86 grams and 2.05 grams of projectile weight have no difference.     State the alternative hypothesis (H1): At 12.5cm and 49 degree stop angle, the flying distance of the projectile using 0.86 grams and 2.05 grams of projectile weight are different.
Step 2: Formulate an analysis plan.	Sample size is 16. Therefore t-test will be used.     Since the sign of H1 is < and > , 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 #2:   Mean (X1): 78.8 Standard deviation (s1): 3.37       State the mean and standard deviation of Run #4: Mean (X2): 68.4 Standard deviation (s2): 5.15 Compute the value of the test statistic (t): n= 16 n1= 8 n2= 8 σ= √((8(3.37)^2 + 8(5.15)^2)/(8+8-2)) =4.652 t= (78.8-68.4)/ 4.652√(1/8 + 1/8) = 4.471   α= 0.05
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 =  ______     3.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 tα = ± 4.471 tα/2 = ± 2.145   As tα = ± 4.471 lies in the rejected region, therefore Ho is rejected.
Conclusion that answer the initial question	Since H0 is rejected, H1 is accepted, this suggests that at a fixed arm length and stop angle, the weight of the projectile has a significant effect on the flying distance of the projectile.
Compare your conclusion with the conclusion from the other team members.	After comparing my results with my teammate Hannah (iron man), I found out that both of our conclusions are the same. Iron man uses runs 1 and 3 for hypothesis testing. H0 is rejected and H1 is accepted.
What inferences can you make from these comparisons?	I can infer that the weight of the projectile has a significant effect on the flying distance of the projectile. As seen in the data collected for our full factorial design, runs 1 and 3 used a (-) arm length while runs 2 and 4 used a (+) arm length. Since Hannah got tα = ±9.0795 while i got tα = ±4.471, this shows that a shorter arm length has a more significant effect on the distance travelled by the flying projectile.
Your learning reflection on this Hypothesis testing activity	Learning hypothesis testing was really confusing for me at the start. It was like learning a new math equation, but I felt that I really had to understand the question and know why each step was taken to solve the tα value. Even though we had practice questions given to us during the CPDD tutorial, by the time I started doing my blog, I had already forgotten most of hypothesis testing and had to ask my peers and Dr Noel questions. I even had to refer to the slides as often as I could for the equation and steps to take. As such, I feel that is important that I practice hypothesis testing every once in a while, as it is an important skill that I may need in the future.