Hypothesis Testing 📊

What is Hypothesis testing? 🤔

A statistical hypothesis 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.

Hypothesis Testing Task 📝

This week we were tasked with applying the hypothesis testing method taught to our results in the DOE practical. Each member from each group had to choose which role they wanted which indicated the run used for the hypothesis testing.

Members:-

Kai rong : Black widow 

Serena : Iron man

Jun xiang : Captain America

Jerome : Hawkeye

Trisyia (Me😊) : Thor - Run #3 from Fractional factorial and Run #2 from Full factorial

Full Factorial data

Fractional Factorial data

The Question

The catapult (the ones that were used in the DOE practical) manufacturer needs to determine the consistency of the products they have manufactured. Therefore, they want to determine whether CATAPULT A produces the same flying distance of projectile as that of CATAPULT B.

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 A and catapult B is collected using the factors below:

Arm length = __28__cm

Start angle = __20__ degree

Stop angle = __60__ degree

Step 1: State the statistical Hypotheses

State the null hypothesis (H₀): Catapult A & B produces the same flying distance of projectile.

State the alternative hypothesis (H₁): Catapult A & B produces different flying distances of projectile.

 Step 2:Formulate an analysis plan

Sample size is _8_ Therefore t-test will be used.

Since the sign of H₁ is _≠_, a left tailed test is used.

Significance level (α) used in this test is __0.05__

Step 3: Calculate the test statistic

State the mean and standard deviation of sample catapult A: 

 Mean (x̄) = 145.5 cm

Standard deviation (σ) = 5.44 cm

 

State the mean and standard deviation of sample catapult B:

 Mean (x̄) = 157.4 cm

Standard deviation (σ) = 3.41 cm

Compute the value of the test statistic (t):

 

n₁ = 8

n₂ = 8

x̄₁ = 157.4 cm

x̄₂ = 145.5 cm

s₁ = 3.41 cm

s₂ = 5.44 cm

v = 8 + 8 – 2

   = 14

Step 4: Make a decision based on result

Type of test (check one only)

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

2.     Right-tailed test: [ __ ]  Critical value t_α =  ______

3.     Two-tailed test: [ _✔_ ]  Critical value t_α/2 = _t_0.975_

                                                                            = _2.145_

 Use the t-distribution table to determine the critical value of t_α or t_α/2

 

 Compare the values of test statistics, t, and critical value(s), t_α or ± t_α/2

Therefore, H_o is __rejected__.

Conclusion that answers the initial question

Since t > t_0.975, H_o is rejected. This means that the alternative hypothesis H₁ that states Catapult A & B produces different flying distances of projectile is correct. This means that the products the company manufactured are not consistent.

Compare your conclusion with the conclusion from the other team members. What inferences can you make from these comparisons?

3 of my members had the same result as me where they also concluded that catapult A & B produces different flying distance whilst 2 of my other members concluded that the flying distances are the same. After discussing with my members, I think that there is still a difference between the flying distance of the two catapults but the difference is not large. Since majority of us concluded that the distances are different, I believe that there is a difference but it is only slight as 2 of my other members concluded the latter.