Blog 5 (Hypothesis Testing)

Hi guys, today I will be sharing about my learning in Hypothesis Testing. So, what exactly is Hypothesis Testing? It is an assumption about a population parameter. This assumption may or may not be true. Hypothesis testing refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.

This was the data obtained from the catapult design for the DOE practical. I will be Person D (Black Widow). Therefore, I will be using Run #4 and Run #8.

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 user will not have any effect on the flying distance of projectile.

Flying distance for catapult is collected using the factors below:

Arm length (A) = ____cm

Projectile weight (B) = _____ grams and ______ grams

Stop angle (C) = _____ degree

State the null hypothesis (H₀):

Using the smaller stop angle (Run #4) and the bigger stop angle (Run #8) results in the same distance travelled by the projectile.

𝜇4 = 𝜇8

State the alternative hypothesis (H₁):

Using the smaller stop angle (Run #4) would have a larger distance travelled by the projectile compared to using the bigger stop angle (Run #8).

𝜇4 > 𝜇8

Sample size is 16 Therefore t-test will be used.

Since the sign of H1 is > , a right tailed test is used.

Significance level (α) used in this test is 0.05

State the mean and standard deviation of Run #4:

Mean: 152.3 cm

Standard Deviation: 3.39 cm

State the mean and standard deviation of Run #8:

Mean: 98.8 cm

Standard Deviation: 2.66 cm

Compute the value of the test statistic (t):

Type of test (check one only)

From the distribution table at v = 14, t(1-0.05) = t0.95 = 1.761

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

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

3.Two-tailed test:[ __ ] Critical value tα/2= ± ______

Comparing the values of test statistics, t and critical value tα:

Since t>tα, we have to Reject Ho.

Therefore Ho is false.

Conclusion that answers the initial question:

Using a smaller stop angle would result in a larger flying distance of the projectile while using a bigger stop angle would result in a shorter flying distance.

Compare your conclusion with the conclusion from the other team members

1. Black Widow [Jeevan]: Using a smaller stop angle would result in a larger flying distance of the projectile while using a bigger stop angle would result in a shorter flying distance.

2. Captain America [Yan Zhen]: Using a smaller stop angle would result in a longer flying distance of the projectile while using a larger stop angle would result in a shorter flying distance

3. Thor [Jeremy]: Using the lighter projectile weight would result in a further distance travelled than the heavier projectile weight.

4. Iron Man [Van Anh]: Using a lighter projectile results in further distance travelled by the projectile, while using a heavier projectile results in shorter distance travelled.

From the above conclusions, we can see that using a smaller stop angle will result in a larger flying distance of the projectile. Furthermore, using the lighter projectile weight would also result in a further distance travelled. Hence, combining both factors would possibly give an even greater distance being travelled.

Here are the links to their blogs!

Yan Zhen: Bing Chilling

Jeremy: Project Mbappe

Van Anh: Guerilla warefare tactics

Inference from these Comparisons

Each of the comparison shows that the distance the projectile travel increases when the LOW (-) value is used. Therefore for a greater travel distance, it is recommended to use the LOW (-) values. This can also be seen from Run #1, which has all the LOW (-) values which gave the furthest distance travelled by the projectile.

Learning Reflection

Before stepping into the class for the hypothesis testing lesson, I was very confused as I had taken a look at the online materials and was very confused. During the lesson, Mr Chua slowly explained to us about the different in population and sample size which gave us a slight understanding about hypothesis testing. However, as he carried on to explain about null hypothesis and the mathematical equations, I got lost. So I decided to go at my own pace and slowly tried to read the notes to get an understanding of what was going on. I realized that this was simply steps on how to check and agree that a hypothesis was correct. It involved the steps of determining if a test is one tailed or two tailed using the signs of the alternate hypothesis. Then using the formula given, we can calculate the test statistic and use the defined acceptance region to determine if we accept or reject the null hypothesis. After understanding the basics of it, I moved on to do the practice questions posted. Mr Chua went through with us the first question which gave me a better understanding of how to solve the question. With that, I decided to give the next few questions an attempt and it went well. I managed to finish the questions rather easily as I grasped the idea of doing them. With that, I would say that I have understood how to do hypothesis testing. Overall, Hypothesis testing is a unique and step by step procedure on accepting or rejecting an hypothesis. It was difficult at first to understand but as I studied it more, I realize that it is pretty easy. This is a really useful technique which I can see myself using in the future for my final year project when formulating a hypothesis.