Project 2 Probability and Statistical Data Analysis by Robby Samudra A19EC0279

Introduction

Education is a very important aspect of life. To advance civilization and improve the quality of life, education is an aspect that must be prioritized. Therefore, I want to learn how the of the quality of education in every country in the Southeast Asia Region. In this research I am more focused on the government's concern for education in financial terms. However, I also noticed how the pattern of  number students and teachers.

Methodology

Dataset was collected from platform called data.un.org and also from (http://statweb.stanford.edu/~sabatti/data.html). The data provided number of students enrolled in three different levels, teachers enrolled in three different levels, also percentage of expenditure on education based on GDP and Government’s expenditure. The target is all 10 countries in Southeast Asia region. The statistical analysis test in this project uses hypothesis testing 2 samples, correlation, regression, and test of independence chi square.

Hypothesis testing 2- sample

            Due to the number of students registered at the primary level is greater than the secondary level. I want to know that with more students enrolled at the primary level compared to the secondary level, there will be more teachers at the primary level. Although at the secondary level the area of ​​teaching expertise is more than the primary level. Therefore I want to determine if there are more teachers at the primary level compared to teachers at the primary level with 5% significance level. The total amount of data from 10 countries in 4 years is 40 for both variables (primary and secondary teachers)

Let µ₁ = Number of teachers in primary is bigger than teachers in secondary level

Let µ₂ = Number of teachers in primary is not bigger than teachers in secondary level

H₀ =µ₁-µ₂=0

H₁ = µ₁>µ₂

Figure 1: R calculation hypothesis 2-sample

H₀ will be rejected if Z₀ > Z_0.05

            Variable X indicates number of teacher in primary level on the other hand variable Y indicates number of teachers in secondary level. Since Z₀ > Z_0.05  we rejected H₀ at 0.05 significance level. there is sufficient evidence that concludes number of teachers in primary level is bigger than teachers in secondary level.

Correlation

Figure 2: R calculation for correlation

The above is the correlation between expenditure on education based on GDP and Government expenditure. Based on the above values ​​between expenditure on education based on GDP and Government expenditure is 0.69926635. we can conclude that there is a moderate relationship between expenditure on education based on GDP and Government expenditure. After we look at this and the results of the correlation between the two, I can conclude between the two that there is a strong relationship which is if there is a change in one variable that can be associated with another change.

Graph  1: Scatter plot of  % expenditure on education based on GDP and Government expenditure.

From the graph we can see expenditure on education based on GDP and Government expenditure. Because here I am using a 1-6 ratio that is low to high. But we can see the level of expenditure on education based on GDP and Government expenditure and show a correlation relationship.

Regression      

Figure 3: R calculation for regression

Graph  2: Scatter plot of students in secondary level and students in primary level

Regression analysis is used to model the relationship between response variables and one or more predictor variables. It can be seen from the graph above that it is a simple regression model involving the response variable y (students in secondary level) and the predictor variable x (students in primary level). because of that he shows the equation ŷ = 32.4515 - 0.6809x, because b0 and b1 are positive and negative there is a positive influence on X₁ and a negative effect on X₂. Value β₀ = 32.4515 which is the intersection coefficient shows the range of .β ₁ = 0.6809_x shows a increases number of students in primary level average for each of students in secondary level by all countries . R2 = 0.9673013 is shown as a moderate relationship between students in secondary level and students in primary level.

Independence of Chi-square

            Chi-square independence test is a procedure for testing if two categorical variables are related in several populations. The 40 samples taken, I want to know any relationship between number of students and teachers in 5 different years.

            H₀ = No relationship between variables

            H₁ = Variables has relationship

Figure 5: R calculation for analysis chi-square 2

Based on the chi-square value obtained, the value of X-squared X² = 64.9964 and its critical value is equal to X²_1,0.05 = 7.814728. since X² > X²_1,0.05 we reject null hypothesis and conclude that there is relationship between students and teachers while in 5 different years.

Conclusion  

            From all of the finding through this analytical study, I can state some conclusion. First, number of students and teachers has a strong relationship. For example, number of students in primary is bigger than number of students in secondary, therefore number of teachers in primary will also bigger than number of teachers in secondary. Second, the correlation between the percentages of expenditure on education by government and GDP have a strong relationship. If the expenditure on education increase then the percentage on both of them will increase. Third, number of students from primary to tertiary level decrease with big difference. It shows us that there is still a lot of students out there who not lucky enough to continue their studies and each country need to take action on this problem. 4. Last, when the expenditure on education increased the number of students enrolled will increased which means we need to spend more for education in addition to uplift the quality of the education.