Hypothesis testing

This blog will cover about hypothesis testing, the hypothesis activity and reflection.

HYPOTHESIS TESTING

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What is hypothesis testing?

Hypothesis testing refers to the formal procedures used by experimenters or researchers

to accept or reject statistical hypotheses.

The best way to determine if a hypothesis is true is by testing the whole population. However, that is almost impossible, hence sample sizes are tested instead.

There are two types of errors that can occur from hypothesis testing:

Type I Error: It occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level (α).

Type II Error: It occurs when the researcher fails to reject a null hypothesis that is false. The probability of committing a Type II error is called Beta (β).

The 4 steps carried out for hypothesis testing are found below:

Step 1: State the statistical Hypotheses

Step 2: Formulate an analysis plan

Step 3: Calculate the test statistic

Step 4: Make a decision based on result

HYPOTHESIS TESTING BLOG ACTIVITY

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Full factorial data from DOE that we will use for hypothesis testing:

Black Widow will use Run #4 and Run#8. To determine the effect of stop angle.

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 user will not have any effect on the flying distance of projectile. Flying distance for catapult A is collected using the factors below: Arm length = 33 cm Projectile weight = 2.06 grams Stop angle = 50 degree and 90 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): There is no effect of stop angle on flying distance of projectile. Flying distance with low stop angle = Flying distance with high stop angle State the alternative hypothesis (H1): There is an effect of stop angle on flying distance of projectile. Flying distance with low stop angle ≠ Flying distance with high stop angle
Step 2: Formulate an analysis plan.	Sample size is n=8 (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	State the mean and standard deviation of Run # 4: mean = 99.9 cm, standard deviation = 0.89 cm State the mean and standard deviation of Run #8: mean = 76.4 cm, standard deviation = 1.92 cm Compute the value of the test statistic (t): n1=8, n2=8 Confidence = 0.95 s1=0.89cm , s2 = 1.92cm X1 =99.9cm , X2= 76.4cm V = n1 + n2 -2 = 8+8 -2 = 14 j b
Step 4: Make a decision based on result	Type of test (check one only) 1. Left-tailed test: [ __ ] Critical value tα = - ______ 2. Right-tailed test: [ __ ] Critical value tα = ______ 3. Two-tailed test: [ _x_ ] Critical value tα/2 = ± 2.145 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 the test statistic t=29.381 lies in the region of rejection, the null hypothesis is rejected and alternative hypothesis is accepted. Therefore Ho is rejected.
Conclusion that answer the initial question	At 0.05 significance, it is found that there is a significant difference in flying distance of the projectile between 50 degree angle and 90 degree angle. Therefore changing the stop angle from 50 to 90 degree will change the flying distance.
Compare your conclusion with the conclusion from the other team members	​My team mate Captain America (Kieron) also rejected the null hypothesis and accepted the alternative hypothesis. Therefore our conclusion is the same.
What inferences can you make from these comparisons?	This shows that changing the stop angle has a signifcant effect on the flying distance of the projectile based on our 2 tests. Moreover, since captain america was comparing 2 runs with low projectile weight and the difference between the mean values of flying distance was larger, it shows that projectile weight and stop angle have a significant interaction.
Your learning reflection on this Hypothesis testing activity	I found hypothesis testing to be very useful. I believe it allows us to carefully evaluate wether our hypothesis is true before implementing it into any data. It is beneficial to experiments as it allows us to see how the population may turn out based on which hypothesis is true. I see myself using this during internship as I will be carrying out many lab experiments, and this would make making a conclusion on the experiment easier.