Mathematics SL Internal AssessmentWhat is the correlation between the countries’ unemployment rate and their crime rates?IntroductionCrime is not a major issue in our residential country, Singapore, with slogans such as “low crime does not mean no crime”. With Singapore’s crime rate ranked as the second lowest globally, I was curious to find what we could credit these low crime statistics to. Usually, we would associate criminals as uneducated, unethical individuals and thus this was why I decided to investigate and find out the relationship between a country’s unemployment rate and their crime rate. With this investigation, we could possibly find the roots of high crime rates in other countries and improve on them.In the process of this investigation, I look into the crime statistics of the the country with the lowest ranked crime rate, Switzerland, and compare them with Singapore against both countries’ crime rate. I specifically chose these countries as these are developed countries found at the bottom of the crime rate rankings. Furthermore, it would be unfair to compare crime statistics between developed and undeveloped countries as the states of these countries would differ, leading to other variables that would affect the country’s crime rate.I was keen to investigate on this after seeing the posters put up by the Singapore Police Force with the slogan “low crime doesn’t mean no crime” during my travels around the country. Thus, this lead me to wonder how Singapore was able to achieve a low crime rate. After thinking about the country’s education system, I thought it should have been the education in Singapore, unemployment rate being a good indicator of that.The aim of this investigation is to find the correlation, if there is, between Switzerland and SIngapore’s crime rate and their unemployment rate. Data from both countries will be collected from a 10 year span between 2006 and 2015. Two possible methods may be implemented in finding a correlation between these two variables, that is if the variables have a linear relationship, I will be using the Pearson’s correlation coefficient. If not, I would be conducting the chi squared test of independence on the two variables gathered to see if the variables influence one another. Collected Data AnalysisWhen looking at the data collected, there is no obvious relationship seen between the two variables when comparing both countries. We observe that in Singapore, the overall number of crime cases increases with the unemployment rate ranging from 1.9% to 2.2%. Further on, we see that the overall number of crimes plateaus with the overall crime rate ranging from 2.5% – 3%. On the other hand, Switzerland’s unemployment rate ranges from 3.4% to 4.8%, significantly higher than that of Singapore’s. However, the range of Switzerland’s overall number of crime cases is smaller ranging from 24000 to 36000.Scatter-plot graphs of the corresponding data have been crafted to observe the individual’s overall number of crime cases against their unemployment rate.Chart 1.1: Scatter Plot Graph showing Singapore’s overall number of crime cases against unemployment rateChart 1.2: Scatter Plot Graph showing Switzerland’s overall number of crime cases against unemployment raAs the investigation aims to compare statistics from both Switzerland and Singapore, I plotted their data on the same graph to find out whether a relationship would be found between the two countries’ crime rate and unemployment rate.Chart 1.3: Scatter Plot Graph showing overall number of crime cases against unemployment rate in Switzerland and SingaporeUpon seeing the plotted graph, there does not seem to be a linear correlation between the points shown on the graph, thus I decided to carry out the Chi-Square Test of Independence with the data collected from the two countries. Chi-Square Test With there being 3 types of analysis falling under the Chi-Square Test, I am specifically looking into the Chi-Square Test of Independence, that is defined as a test for determining whether two variables are independent. If the null hypothesis is not obtained when testing, the variables are not independent and thus have a relationship or are associated to each other.The chi-square test of independence involves four steps to find a relationship between these two variables or otherwise.These four steps include;Stating the hypothesesTwo sets of hypotheses may be crafted prior to carrying out the chi square test on a set of data, that is null or alternative. Firstly, the null hypothesis suggests that you may not predict one of the variables by observing the level of the other variable as they would not be associated. The alternative hypothesis, on the other hand, suggest that there is a relationship between the variables and thus you may be able to predict one variable’s level by observing the other.Formulating an Analysis PlanThis analysis plan describes how the data is used to reach the alternative or the null hypothesis. This includes stating the significance level and identifying the test method to be the Chi-Square Test for independence.Analyzing the sample dataWith the data collected, the degree of freedom must be obtained. The degree of freedom refers to the number of values that are free to vary in the final calculation of statistics. The degree of freedom is obtained using the equation below.DF = (r – 1) (c – 1)In the equation above, R refers to the number of rows while C refers to the number of columns in the final calculations.Furthermore, the expected frequency counts of each cell of the collected data need to be calculated as expected frequency counts refer to the projected value in each cell if the null hypothesis were to be true. To calculate the expected frequency of each cell in the collected data, the formula below is used. Er,c = (nr * nc) / nIn the case of this investigation, Nr would be the total number of observed data in a row, while Nc refers to the total number of the data in a column. Finally N is referred to as the total sample number. An example of the Nr and Nc can be found below Next, the test statistic is obtained, that is a random chi square variable defined by the equation below. ?2 = ? (Or,c – Er,c)2 / Er,c Or,c refers to the observed value of either total number of Crime cases or the employment rate in one cell while Er,c is the expected frequency count of that same cell.Lastly, the P value is obtained from the Chi-square distribution calculator.Interpreting the ResultsWith the significance level and the P value in hand, we may now be able to reject the null hypothesis or otherwise when corresponding the values on the Chi-square distribution table. Carrying out Chi-Square TestHypothesisNull Hypothesis – Both overall number of crime cases and unemployment rate in both countries are independentAlternative Hypothesis – The overall number of crime cases is dependent on the unemployment rate of the country in a given year.Using the formula below, I calculate the expected count of both the overall number of crime cases and unemployment rate for every cell.With the processed data above, I now craft a frequency table depicting both average observed and expected overall crime cases with the corresponding ranges of unemployment rate.