Hypothesis Testing

 Hypothesis Testing

Group members: 
  • Nander (Iron Man)
  • Tzer (Thor)
  • Ashwati (Captain America)
  • Daryl (Hulk)
  • Nikkisha (me, Black Widow)

Full factorial data

Fractional factorial data


Iron Man to use Run 2 from FRACTIONAL factorial and Run 2 from FULL factorial.

Thor will use Run 4 from FRACTIONAL factorial and Run 4 from FULL factorial.

Captain America will use Run 5 from FRACTIONAL factorial and Run 5 from FULL factorial.

Hulk will use Run 4 from FRACTIONAL factorial and Run 4 from FULL factorial.

Black Widow (me) will use Run 7 from FRACTIONAL factorial and Run 7 from FULL factorial.

The QUESTION

The catapult (the ones that were used in the DOE practical) manufacturer needs to determine the consistency of the products they have manufactured. Therefore they want to determine whether CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

 

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 A and catapult B is collected using the factors below:

Arm length =  _28_cm

Start angle = _20__ degree

Stop angle = __90_ degree

 

Step 1:

State the statistical Hypotheses:

State the null hypothesis (H0):

Ho :m1 = m2

 

 

State the alternative hypothesis (H1):

H1 :m1 ≠ m2

 

 

 

 

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 sample catapult A:

x̄1 = 82.9

S1 4.3

 

 

State the mean and standard deviation of sample catapult B:

x̄2 = 90.4

S2  = 3.07

 

Compute the value of the test statistic (t):

 

 

V = 8 + 8 – 2 = 14

δ = 3.99

t = -3.75

 

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: [ _ü_ ]  Critical value tα/2 = ± _ 2.306 _

 

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

t = -3.75 lies in the rejection zone

 

 

Therefore Ho is _Rejected___.

 

 

Conclusion that answer the initial question

 

Both catapults did not project the same distance travelled at significance of 0.05.

 

 

 

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

 

What inferences can you make from these comparisons?

The comparisons we had are quite similar, where the catapults did not give off the same results.

Reflection 

During this practical, we have used full factorial and fractional factorial to identify the most significant and least significant factors that contributed to the differences in results. We used this skill that we learnt onto our class activity challenge and our performance reflected well on our workings. I will definitely make full use of this useful method in the future such as for my Capstone project.

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