Hypothesis Testing
In this blog, I will be sharing about my assigned Hypothesis Testing task👀.
What is Hypothesis Testing?
Hypothesis testing is an ideal way to determine if a statistical hypothesis is true. Hypothesis testing is conducted on a random sample of the population to accept or reject a statistical hypothesis.
Task
For this task, I am Person B (Thor)🔨. I will be using Runs #2 and #4 to determine effect of projectile weight👀.
This is my group's full factorial practical data.
📎Calculation
The QUESTION | To determine the effect of projectile weight on the flying distance of the projectile.
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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 the projectile.
Flying distance for catapult is collected using the factors below:
Arm length = 22.5 cm Projectile weight = 0.87 grams and 2.01 grams Stop angle = 60°
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Step 1: State the statistical Hypotheses: | State the null hypothesis (H0):
X1 = X2
An increase in projectile weight has no effect on the flying distance of the projectile.
State the alternative hypothesis (H1):
X1 > X2
An increase in projectile weight decreases the flying distance of the projectile.
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Step 2: Formulate an analysis plan. | Sample size is 2 < 30. Therefore t-test will be used.
Since the sign of H1 is > , a one-tailed (right) test is used.
Significance level (α) used in this test is 0.05.
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Step 3: Calculate the test statistic | State the mean and standard deviation of Run #2 :
X1 = 185.8 cm Standard deviation = 2.84 cm
State the mean and standard deviation of Run #4 :
X2 = 161.1 cm Standard deviation = 3.72 cm
Compute the value of the test statistic (t):
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Step 4: Make a decision based on result | Type of test:
From t-table, when v = 14, t at 95% distribution level = 1.761. Since the test statistic, t = 13.96, lies in the rejection region, the null hypothesis is rejected. Therefore Ho is rejected.
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Conclusion that answer the initial question | Since the test statistic, t = 13.96, lies in the rejection region, the null hypothesis is rejected. At 0.05 level of significance, an increase in projectile weight, from 0.87 g to 2.01 g, decreases the flying distance of the projectile.
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Compare your conclusion with the conclusion from the other team members.
| Wei Ling's:
Based on t-distribution table, critical value for t distribution of 95% and v = 14 is 2.154. t is outside of t distribution curve, therefore stop angle has an effect on flying distance of projectile.
Ethan's:
Since the critical value of t when there is distribution of 95%, v = 14 is 1.761. t is in the rejection region and therefore, Ho is rejected as it lies in the region of rejection. I conclude that the use of a lighter projectile would result in a larger flying distance of the projectile while using a heavier projectile would result in a shorter distance flown.
Jing Yang's:
Since Ho is rejected, H1 will be accepted. Hence, at constant setting for arm length and projectile weight, the flying distance of the projectile reduces when the stop angle increases from 60° to 90°.
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What inferences can you make from these comparisons?
| - Firstly, an increase in stop angle, leads to a decrease in the projectile flying distance.
- Secondly, an increase in projectile weight, leads to a decrease in the projectile flying distance.
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💭Learning Reflection
During the tutorial lesson, I was introduced to hypothesis testing👀. I learned that there is a systematic way to carry out hypothesis testing as seen from the table above. This systematic method helped me to perform my calculations methodically and at the same time, understand what I am calculating. The practice questions that I did in class allowed me to practice identifying what are the means, standard deviations and sample size. One of the challenges that I encountered was forming the null hypothesis and alternative hypothesis😵. This is an important step as it is the first step in the calculations and hence it is important to master it. By attempting the practice questions, I get to expose myself to different types of questions and the three different t-tests; one-tailed (right) test, one-tailed (left) test and two-tailed test. I learned that forming the alternative hypothesis is important as the different mathematical symbols; <, >, or ≠ determines what t-test to conduct. Furthermore, through this task, by applying the hypothesis testing concepts to complete this task using my group’s full factorial practical data, I get a better understanding of how to apply hypothesis testing on my own👍. After completing this task, I am more confident to conduct hypothesis testing as I am able to grasp the concept👻.
