Blog Entry 5: Hypothesis Testing
For this blog, my group members' respective characters are:
I am Iron Man
Clive is Thor
Adyl is Hulk
Joelle s Black Widow
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So in this blog I will be going over how to determine how the projectile weight affects the projectile flying distance (from blog 4).
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Different user will not have any effect on the results as we are assuming that the human affect is negligible. The flying distance of the catapult was collected using the factors:
Arm length of 28cm
Projectile weight of 0.89g to 2.01g
Stop angle of 90°
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The null hypothesis would be that at an arm length of 28cm and stop angle of 90°, the projectile flying distance at a projectile weight of 0.89g and 2.01g has no difference.
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The alternative hypothesis is that at an arm length of 28cm and stop angle of 90°, the projectile flying distance at a projectile weight of 0.89g and 2.01g has a difference.
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A t-test will be used since the sample size is for the 0.89g runs is 8 and 2.01g runs is also 8.
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Since the sign of the alternative hypothesis is "≠", a two tailed test is used and a significance level of 0.05.
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The standard deviation of run 1 is 6.84.
The standard deviation of run 3 is 1.22.
Using the equations above, I calculated a
t value of -0.228476
v value of 14
Looking at the t distribution table of t at 97.5% level of confidence, the critical t values is -2.145 and 2.145. The reason you take the t value of a level of confidence at 97.5% is cause for a two tailed test, there are two critical values but you still need that acceptance region to be 95% due to 5% level of significance. Thus, the level of significance is 2.5% + 2.5%.
As you can see from the graph, the calculated t value falls within the acceptance region. Therefore, the null hypothesis is accepted and the projectile weight does not affect the projectile flying distance.
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Based on the step done, it states that changing the projectile weight will not affect the projectile flying distance.
However from experience, I believe that the weight of the projectile should affect the flying distance. During the DOE practical when my group was doing the challenge where we launch the projectile at cut-outs of lecturers, there was one attempt where our projectile was not able to reach Dr Noel. To solve it, I changed the projectile to a lighter weight and the projectile hit him right in the head (lol). Thus, I believe that this is Type II error where the null hypothesis is false but it was failed to be rejected.
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There were two other group members who did their hypothesis testing on how the projectile weight affects the projectile flying distance, Clive and Adyl.
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Clive's result was accepting the null hypothesis, the same conclusion as mine. However, the reasoning for this was due to the fact that one of the data points he used in his samples was skewed and considered an anomaly. This caused his calculation of his t-value to go into the acceptance region. He also possibly has a Type II error.
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Adyl's result was rejecting the null hypothesis, meaning that the projectile weight does affect its flying distance which is the correct answer.
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After discussing with them, we came to a conclusion that the projectile weight is supposed to affect the projectile flying distance.
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As for the remaining member of my group, Joelle, she did her hypothesis testing on how the stop angle will affect the projectile flying distance. She rejected her null hypothesis, therefore the stop angle affects the flying distance.
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When it comes this topic, I feel the same way about it as DOE. I think things are related to analysing data, I will like it. There is also probably an added interest in these topics because I will need to use them in what I want to work as in the future, so I really do not mind doing all these practices as compared to some modules which I really have no interest in cause I'm probably never gonna work in that industry... (I am definitely not gonna take chemical engineering in uni...). I did not know that there was a way to test a hypothesis. I always thought you just look at the data and if then conclude there is a correlation or not. I guess I also felt similar when I was doing the DOE as well. Overall, I feel like I have learnt a good amount for the last two topics and can foresee myself using them in the future.