Hypothesis testing

 Hi everybody, I'm back with my 5TH blog!!!!

What is Hypothesis Testing?

Hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.

A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true.

2 types of statistical hypothesis:

1) Null Hypothesis (H0) states that differences in sample observations result purely from chance and that there is no statistically-significant difference in a set of given observations.

2) Alternative Hypothesis (H1) states that differences in sample observations are statistically-significant and influenced by some non-random causes.

Hypothesis testing is used to answer questions such as:

-  Is the new material as strong as the old one?

-  Is the performance of our product enhanced after undergoing the revamp?

-  Does our product last longer than that of our competitors?

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

1. Ryan (Iron Man)

2. Hai Teng (Thor)

3. Fion (Captain America)

4. Isabella (Black Widow)

5. Wayne (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 =  27 cm Projectile weight = 0.86 grams and 2.06 grams Stop angle = 72 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The effect of projectile weight on the flying distance of projectile is non-significant.     State the alternative hypothesis (H1): The effect of projectile weight on the flying distance of projectile is significant.
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 (X1): 191.8 Standard deviations (S1): 3.02       State the mean and standard deviation of Run #8: Mean (X2): 185.6 Standard deviations (S2): 3.58       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 =  ______ 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  Since t = ±3.502, which lies in the rejected region, this shows that projectile weight affects the flying distance of the projectile. Therefore Ho is REJECTED.
Conclusion that answer the initial question	Ho is rejected and H1 is accepted. This shows that the effect of projectile weight on the flying distance of projectile is significant.
Compare your conclusion with the conclusion from the other team members.	My teammates, Ryan (Iron Man) and Hai Teng (Thor) arrived at the same conclusion that the null hypothesis and the alternate hypothesis is accepted. This suggests that effect of projectile weight on the flying distance of projectile is significant.
What inferences can you make from these comparisons?	Reduce the projectile weight in order to increase the flying distance of the projectile.
Your learning reflection on this Hypothesis testing activity	At first, I am really clueless about Hypothesis Testing. After the lesson and attempting the 4 practice questions, I kind of grasped the concept about the null and alternative hypothesis, and through analysing and calculation, we have to reject either null or alternative hypothesis. Through the hypothesis testing, I can differentiate which hypothesis is true or false.