Example Of Experiment For Statistical Study Case Study

Introduction

In this paper I will show the basic concepts of statistics and probability theory application related to a real world problem. The goal of this assignment is to conduct an experiment for statistical study and perform four steps mentioned in assignment instructions.

Body

Assume in a particular college there was performed a statistical research. The researchers observed how the graduate students passed a final exam in mathematics and physics. The result of exam was evaluated from 0 points to 100 points for each discipline. The researchers took 40 students at a random and recorded their results in both exams. There are three variables in this research:
ID – the number of the student observed

Math – a result in final mathematics exam

Physics – a result in final physics exam
The observations are given below in the table:
The researchers are interested is there a significant difference between average grade in mathematics and average grade in physics for those who have passed the final exams.
I begin with hypothesis formulating.

Null hypothesis: There is no significant difference between the grades in final exams.

Alternative hypothesis: There is a significant difference between the grades in final exams.
H0: μ1=μ2Ha: μ1≠μ2

Set level of significance alpha at the most common for researches level of 5%:

α=0.05
It’s time to select the test for checking the hypotheses. I claim that two-sample Student’s t-test is appropriate here. Since I don’t know the population standard deviation, z-test is not useful. The main assumption of student’s test is normality for the sample distribution.
There are many different techniques to check the distribution of a sample. In our case I just take a look at the distribution on a graph. Consider frequency histograms of the sample distributions:
A blue bell-curved line represents normal (Gaussian) distribution. I conclude, that the sample distribution for both samples is close to normal, thus, t-test is appropriate.

Perform testing and construct 90% confidence interval for the difference between mean values of the samples:

Two-Sample T-Test and CI: Math; Physics
Two-sample T for Math vs Physics
N Mean StDev SE Mean
Math 40 71,8 12,9 2,0
Physics 40 63,6 29,7 4,7
Difference = mu (Math) - mu (Physics)

Estimate for difference: 8,25

90% CI for difference: (-0,33; 16,83)
T-Test of difference = 0 (vs not =): T-Value = 1,61 P-Value = 0,113 DF = 53
Since p-value of the test is greater than 0.05, I failed to reject the null hypothesis. I have no evidence to say that the average grades in math and physics are significantly different (at 5% level of significance).
A 90% confidence interval is (-0.33, 16.83). I’m 90% confident that a difference between population averages of the grades is between -0.33 and 16.83 points