Blog 4: Hypothesis Testing

Hi again! If you are wondering why 2 blogs are up within 2 days time, I am literally doing these blogs back to back. Today I will be covering the topic of Hypothesis Testing. Below will be the some of the content I will be covering.

Content:

1. Theory

2. Put it into practice

3. Learning Reflection

Theory for Hypothesis Testing

What is hypothesis testing?

• A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true.

• refers to the formal procedures used by experimenters or researchers to accept or reject statistical hypotheses.

• The ideal way to determine if a statistical hypothesis is true or false by examining the entire population. However, such a process is very time-consuming and impractical so researchers usually examine a random sample from the population.

• However, this may lead to decision errors

What are decision errors?

• They occur when the sample is not a true reflection of a population.

• Decision errors are categorised in 2 categories.

1. Type 1 errors

2. Type 2 errors

Steps involved in Hypothesis Testing

1. State the statistical hypotheses.

2. Formulate the analysis plan (for this blog, focus mainly on t-test)

3. Calculate the test statistics (math)

4. Make a decision based on results (accept or reject null hypothesis)

Putting it into practice

Data:

The QUESTION	To determine the effect of projectile weight 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 = 28cm Projectile weight = 0.86 grams and 2.08 grams Stop angle = 45 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): At 28cm arm length and 45˚ stop angle, the flying distance of the projectile using 0.86g projectile weight and 2.08g projectile weight are not different. μ=μ0 State the alternative hypothesis (H1): At 28cm arm length and 45˚ stop angle, the flying distance of the projectile using 0.86g projectile weight and 2.08g projectile weight are different. μ≠μ0
Step 2: Formulate an analysis plan.	Sample size is less than 30. 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
Step 4: Make a decision based on result	Type of test: Left-tailed test: [X]  Critical value tα = Nil Right-tailed test: [X]  Critical value tα = Nil Two-tailed test: [O]  Critical value t0.975 = ± 2.447 Use the t-distribution table to determine the critical value of tα or tα/2 Compare the values of test statistics, t, and critical value(s), tα or ± tα/2 Since t>t0.975 so t is outside the range between - t0.975 and t0.975 therefore Ho is rejected.
Conclusion that answer the initial question	Since Ho is rejected, H1 is proven to be true. Therefore, at 28cm arm length and 45˚ stop angle, the flying distance of the projectile using 0.86g projectile weight and 2.08g projectile weight are different. Thus, projectile weight effects the flying distance of the projectile.
Compare your conclusion with the conclusion from the other team members.	Yu Jie: He is doing the same question as me and from his results, the results shows that the test statistic is outside the acceptable range so the null hypothesis is rejected and the alternative hypothesis of projectile weight affecting flying distance of projectile is accepted. Dhasna:She is doing the effect of stop angle on flying distance of projectile and from her results, the test statistic is in the acceptable range so her null hypothesis of stop angle of not affecting flying distance is accepted. Mabelle: She is doing the same question as Dhasna and her results back up the conclusion of Dhasna from her results, the test statistic is in the acceptable range so her null hypothesis of stop angle of not affecting flying distance is accepted.
What inferences can you make from these comparisons?	To increase the flying distance of the projectile, decrease the projectile weight. Stop angle does not affect the flying distance of the projectile.

Learning Reflection

When Mr Chua first introduced to us Hypothesis Testing, I thought it was a very straightforward process where I just have to see if the value of the dependent variable increase or decrease when I alter the independent variable. However, I realised I had to use complex formula and use terms such as standard deviation that I have not touched since my E Math O level days.

One of the challenges faced was determining which type of test to use as I was confused when to use the one-tailed test and the two-tailed test. One tailed test is used to determine if there is a significant difference in one direction and two tailed test is used to determine if there is a significant difference in both direction. The type of test matters as they are used to determine the test statistic which could affect the result of accepting or rejecting the null hypothesis.

This knowledge of hypothesis testing will be useful for me in the future especially when I am doing my Final Year Project (FYP), when I am doing my FYP, I will be developing a product and such a product would need to undergo experiments to finetune the product so I would need to know the relationships between the dependent and independent variables. This would allow me to apply what I learnt during this hypothesis testing as through all the equations and test in this hypothesis testing, I would be able to know what variables would not affect the efficiency of my product and the variables I have to alter to ensure my product is of quality.

This is the end of the blog! See you next time!

Next blog is the last blog so stay tune for our tea maker prototype!