Hypothesis Testing

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 Hypothesis Testing



For this blog,we will be doing hypothesis testing based on our DOE practical.

For the DOE practical,my teammates consisted of

  1. Kieran Lee (Black Widow)

  2. Anwar (Iron Man)

  3. Katrina (Thor)

  4. Jun Lin (Hulk)


Full factorial data table


Fractional factorial data table

Since I am doing black widow for this experiment, I will use run #8 from Full factorial and run #8 from Fractional factorial.


Catapult A is used in the Full Factorial run while Catapult B is used in the Fractional factorial run 


The Question:

The manufacturer needs to determine the consistency of the catapult they have manufactured.Hence they would like us to determine whether Catapult A produces the same flying distance of projectile as that of Catapult B.


Scope of the test:

The human factor in both catapults are assumed to be negligible.Therefore different users will not have any effect on the flying distance of the projectile.


Flying distance for catapult A and catapult B is collected using the factors below.


Arm length of 34cm

Start Angle of 30°

End Angle of 90°


The Statistical Hypothesis:


The null hypothesis:
Catapult A and Catapult B produce the same flying distance.


Alternative hypothesis:

Catapult A and Catapult B does not produce the same flying distance


Analysis plan:

Since sample size is 8,t-test will be used


Test Statistic:


The mean and standard deviation of sample catapult A for run #8 is:


Mean: 90.4cm

Standard Deviation: 1.53cm


The mean and standard deviation of sample catapult B for run #8 is:


Mean: 87.9cm

Standard deviation: 2.78cm


Compute the value of the test statistic (t):

t=X1-X21n1+1n2

v=n1+n2-2

=n1s12+n2n1+n2-2


X1=90.4cm

X2=87.9cm

S1=1.53

S2=2.78

n1=8

n2=8


By substituting the values above into the formula, we get:


=2.398

v=14

t=2.085

Determine type of test:

A two tailed test will be used.

We will be using a significance level of 0.05

2 tail: 0.05/2 = 0.025

Therefore,t0.975

When V =14,t0.975= 2.292


Conclusion

Since t>t0.975, t lies within the acceptable region,thus null is accepted. At 0.05 of significance level, both catapults produce the same flying distance.


Teammates conclusion


Anwar:Both catapults produce the same flying distance and the null hypothesis is true


Katrina:Both catapults produce the same flying distance and the null hypothesis is true


Jun Lin:Both catapults produce the same flying distance and the null hypothesis is true.


From the multiple conclusions the team obtained,we can infer that both catapults produce the same results and hence both the catapults are consistent.


Reflection

After going through the lesson hypothesis testing,I learned more about hypothesis testing and how it is used by researchers as a formal procedure to accept or reject statistical hypotheses made by researchers.Hypothesis testing can be used to answer questions that we are trying to find out and whether it matches with our hypothesis. The best way to test a hypothesis is to examine the entire population.However,this if often unrealistic and impractical,we can examine a random sample from the population to keep the results fair and unbiased.If the random sample data is different from the hypothesis,the hypothesis is rejected as the data does not support our hypothesis.


There are 4 main steps in hypothesis testing to get our decision.

  1. State the statistical hypotheses

  2. Formulate an analysis plan

  3. Calculate the test statistic

  4. Make a decision based on results.


Firstly, we would need to state our statistical hypotheses.The hypotheses stated are mutually exclusive.Thus,if one hypothesis is true,the other hypothesis is false.We have two types of hypotheses.

  1. Null Hypothesis

  2. Alternative Hypothesis


Null Hypothesis:Difference in sample results are purely due to chance and there is no statistically-significant difference in the set of observations


Alternative Hypothesis:Differences in sample results are statistically-significant and influenced by some non-random causes.


Secondly,an analysis plan will help us determine which statistical test will be used.There is a one tailed test and a two tailed test.


Next,we would need to calculate the test statistic to find the value of t.


Lastly, we would need to do decision making.A hypothesis is accepted or rejected based on whether it is in the acceptance region or rejection region.


If the results are in the acceptance regions,the null hypothesis is accepted and not rejected.


If the results are in the rejection region,the null hypothesis is rejected.


Hypothesis testing can help us in our future experiments to determine whether our hypothesis is correct.

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