Hypothesis Testing

Hypothesis Test 

For this practical, I am taking on the role of Captain America where I will be using Runs 2 and 6 to investigate the effect of the stop angle on the catapult. 


This were the limits set by my group for the factors during the practical session:




Below is the data we have obtained for Full Factorial Design:


The Question 

To determine the effect of stop angle on the flying distance of the projectile


Scope of the test 

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


Flying distance for catapult is collected using the factors below:


Arm length = 33cm 

Projectile weight = 0.8619 grams

Stop angle = 10 and 40 degree


Step 1:


State the statistical hypotheses: 

Null Hypothesis (H0): 

Using projectile weight of 0.8619 grams, arm’s length of 33 cm and 2 different stop angles of 10 and 40 degrees, the distance of the projectile launched from the catapult into the sandpit will have no effect meaning it will be the same. 

μ2=μ6


Alternative Hypothesis (H1):

Using projectile weight of 0.8619 grams, arm’s length of 33 cm and 2 different stop angles of 10 and 40 degrees, will be different meaning that there will be an effect. The projectile in run 2 (lower stop angle) will be able to travel a larger distance. 


μ2>μ6


Step 2:


Formulate an analysis plan 

Sample size is 16. Therefore, t-test is used.


Sign of H1 is > (Right-tailed) 

Significance (α) used in this test is 0.05. 

Step 3:


Calculate the test statistic 

State the mean and standard deviation for Run #2: 

Mean= 87.1

SD= 1.55


State the mean and standard deviation for Run #6: 

Mean= 46.1

SD= 0.90 


Compute value for test statistic (t) : 

t= 60.525

Step 4: 


Make a decision based on the result 



Type of test (check one only)

  1. Left tailed test [   ] Critical value tα = -

  2. Right tailed test [ ✔   ] Critical value  tα =1.761

  3. Two tailed test [    ] Critical value tα/2 = 


Using the 95th percentile, tα =1.761


Therefore, Ho  is rejected as the value of t calculated in the previous step is in the rejected region. 


Conclusion that answers the initial question 

Since Ho  is rejected, this means that the projectile weight will have an effect on how far it can be launched onto the sand pit. This means that H1 is accepted. 

Compare your conclusion with the conclusion from your other team mates 

Using Darel’s(He is person D) data to compare, it can be concluded that Ho  should be rejected. 


You can refer to his blog here. 

What inferences can you make from these comparisons? 

This means that we can conclude that different angles will have an effect on the distance that the projectile can be launched. 

Learning reflection 

When I first heard the words ‘Hypothesis Testing’ I thought it was just going to be a recap of what we did back in secondary school which would just be forming simple statements such as ‘The higher the temperature, the higher the rate of reaction’ (something like that) BUT I WAS VERY WRONG 😭😭😭 


It was a lot more complicated than just simple statements😰. At first, I only thought that there was only one kind of hypothesis that could be formed, which was the one above (which would be similar to an alternative hypothesis). However, there is also the Null Hypothesis which is basically just saying that the dependent variable has no effect. 


Additionally, we also have to consider other factors like significance and tailed tests which will help us come to our conclusion.


Since all these factors were new to me, I obviously struggled. But as I did the practice questions, it made me realise that Hypothesis Testing helps us deal with large amounts of data and also helps us gauge whether we have to reject our hypothesis or not. 


The practical session also helped me integrate 2 concepts together being DOE and Hypothesis testing. It made the learning process more fun as not only were we just collecting data, we also had to utilise the data for the group challenge (which I mentioned in my DOE entry) and the blogs which helped me reinforce my concepts. 


It definitely made me realise that Hypothesis testing can be quite useful and in fact powerful as it can pretty much most of the time. I look forward to utilising it more 😁😁 

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