Hypothesis Testing

 Welcome back to my blog!!

 

Today I’ll be sharing with you all on my journey of understanding hypothesis testing.

Hypothesis testing is whereby there will be an assumption about a parameter that will be tested out using statistics. When testing out a hypothesis, it is usually ideal to test out the entire population size. However, it is impractical to do so, this results in only having a small sample size from the population.

If the sample data does not coincide with the statistical hypothesis, the hypothesis is reject.

Decision errors

When using a sample size, it does not represent the entire population, this may lead to decision errors.

Here are the 2 types of error:

Type I error: This is when the researcher rejects a null hypothesis when it is true. The probability of having a type I error is called the significane level (α) 

Usually, the significance level would be lower when it comes to health science or hospital cases. A more stringent significant level of 0.01 would be used

Type II error: This is when the researcher fails to reject a null hypothesis that is false. The probability of having a type II error is called Beta (β)

DOE PRACTICAL TEAM MEMBERS:

Iron Man: Reinard

Thor: Clive

Black Widow: Joelle (Me 😊)

Hulk: Adyl

 

Data collected for FULL factorial design using CATAPULT A (fill this according to your DOE practical result):

Run#	Run Order	A	B	C	D=AB	E=AC	F=BC	G=ABC	R1	R2	R3	R4	R5	R6	R7	R8	Ave.	Std.Dev.
1	7	-	-	-	+	+	+	-	116.0	95.0	100.0	99.5	100.5	95.5	95.0	99.0	100.1	6.84
2	5	+	-	-	-	-	+	+	109.5	107.0	100.0	105.0	100.0	115.5	115.0	104.0	107.0	6.02
3	8	-	+	-	-	+	-	+	99.0	97.5	98.0	101.0	100.0	100.0	100.0	100.5	99.5	1.22
4	4	+	+	-	+	-	-	-	105.0	109.0	109.0	137.5	104.0	106.5	115.5	103.0	111.2	11.34
5	1	-	-	+	+	-	-	+	234.0	230.0	233.0	232.0	229.0	235.0	233.5	232.0	232.3	2.02
6	6	+	-	+	-	+	-	-	173.5	190.0	181.5	185.5	183.0	191.0	187.0	188.5	185.0	5.68
7	2	-	+	+	-	-	+	-	210.0	211.0	215.5	213.5	207.0	214.5	213.0	220.5	213.1	4.03
8	3	+	+	+	+	+	+	+	174.0	175.0	176.0	175.0	177.0	171.5	168.0	173.5	173.8	2.85

 

Iron Man will use Run #1 and Run#3. To determine the effect of projectile weight.

Thor will use will use Run #2 and Run#4. To determine the effect of projectile weight.

Captain America will use Run #2 and Run#6. To determine the effect of stop angle.

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

Hulk will use Run #6 and Run#8. To determine the effect of projectile weight

 

 

 

 

 

 

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 = 33.2 cm Projectile weight = 2.01 grams Stop angle = 90 degree and 120 degree
Step 1: State the statistical Hypotheses:	State the null hypothesis (H0): The Stop Angle of the catapult has no significant effect on the flying distance of the projectile.     State the alternative hypothesis (H1): The Stop Angle of the catapult has a significant effect on the flying distance of the projectile.
Step 2: Formulate an analysis plan.	Sample size is 8 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:111.2 Standard deviation:11.34     State the mean and standard deviation of Run #8: Mean: 173.8 Standard deviation: 2.85       Compute the value of the test statistic (t):       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 tα = - ______ 2.    Right-tailed test: [ __ ]  Critical value tα =  ______ 3.    Two-tailed test: [ _✅_ ]  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 ± tα/2 = ±2.145 t = -14.166 Therefore, Ho is Rejected.
Conclusion that answer the initial question	At 0.05 level of significance, it is found that there is a significant difference in the flying distance of the projectile between 90 degree and 120 degree stop angle.
Compare your conclusion with the conclusion from the other team members.	Due to the lack of forward planning, no other team member in my group did hypothesis testing on the effect on stop angle. However, when I cross checked with the other groups, the Null Hypothesis was also rejected.
What inferences can you make from these comparisons?	When comparing with the other groups data as well as mine, there is a significant effect when the stop angle changes. This is supported as both Null Hypothesis was rejected and the Alternative Hypothesis was accepted.
Your learning reflection on this Hypothesis testing activity	During this activity, it helped reinforce my learning as well as understanding from the tutorial class. This is because during the tutorial class, I personally could not understand why we had to learn this. Despite the practice questions given to us to try, for me it was more of understanding what the numbers meant instead of actually understanding what the number implies.   However with this particular activity, it strengthen my understanding and taught me what it actual means to apply hypothesis testing.   This activity also taught me that just based off 2 runs, I am able to have a rough idea on the relationships of the parameters. This is because based off runs 4 and 8, I am able to deduce that when there is a change in stop angle, there will be a change in the distance that the projectile travelled.   After going through this activity, I hope that I would be able to apply for any up coming projects that requires me to study the effects on a singular parameters better. This is because this is an easy way to test out if the parameters do have an effect.