Mathematics

Theory Foreign aid is defined as the assistance in money that a specific country transfers to another country. Those, as mentioned above, can assume the form of a gift, loan, or grant. Foreign aids have the capacity within the context of contributing to the engagement with civil society and democratization through the provision of assistance attached with the strengthening of the executive powers, the process of election, improvement of education, and increase of the per capita income. There is less evidence on the factors affecting the promotion of foreign aid towards democratization. There is further evidence on the fact that there exist few society organizations have a direct engagement attached to the process of policy formulation and making an impact on the outcome of policy. On the other dimension, there is further less information provided within the literature review on how democratization is influenced by foreign aid. On the different aspect, there exists limited research that is attached to the relationship that exists between the civil society organization that operates in the countries that receive foreign aid. Hypotheses H0: The determinant factors contribute to democratization and the engagement and civil society engagement in receiving democratic aid.  H1: The determinant factors don’t contribute to democratization and the engagement and civil society engagement in receiving democratic aid. Unit of Analysis  The unit of analysis will be country-year of states receiving foreign aid. This unit was chosen to determine if there is a relationship between the years that states receive foreign aid and CSO participation and democratization over the same years. Independent variable Foreign Aid – https://data.worldbank.org/indicator/DT.ODA.ODAT.PC.ZS Net official development assistance (ODA) per capita consists of disbursements of loans made on concessional terms (net of repayments of principal) and grants by official agencies of the members of the Development Assistance Committee (DAC), by multilateral institutions, and by non-DAC countries to promote economic development and welfare in countries and territories in the DAC list of ODA recipients CSO Strength – Civil Society Participation Index measures if CSOs are routinely consulted by policymakers, their involvement of people in CSOs, including women, and if legislative candidate nomination within party organization is highly decentralized or made through party primaries. Dependent variable  Democracy indicies – indices measure the extent that electoral, liberal, participatory, deliberative, and egalitarian democracy has been achieved. Using this information, we can measure improvement in democracy in states where more established CSOs are active. Questions: 1) Conduct a basic bivariate hypothesis test showing the relationship between your independent variable and your dependent variable. Explain why you chose the test you did, and what it shows. 2) Are there reasons this hypothesis test may not tell the whole story? What are they? Control Variables 3) Consider three to five (3-5) alternative explanations for changes in your dependent variable that could confound your explanation of interest (i.e., variables that may lead to omitted variable bias). Write these out in terms of formal null/alternative hypotheses. 4) Find data to operationalize these controls. Paste histograms/bar charts/summary statistics (as appropriate) of the relevant variables

Mathematical principles and computations are used everyday in all aspects of life. Over the years and with major computational advancement, mathematicians have developed simple and easier methods for more challenging and advanced computations with double-precision floating-point accuracy. However, a higher level of numeric precision is required and is more beneficial in certain applications in the scientific and engineering field. This paper presents examples of these applications and analyzes the techniques used to provide high-precision arithmetic. We conclude that high-precision numerical computation softwares are necessary for the modern expansive and demanding problems.

This journal assignment will allow you to reflect on your own experiences as a mathematician. Your experiences affect your perspectives about learning and teaching mathematics.Please share your emotions, attitudes, and beliefs about mathematics and what your mathematical experiences mean to you, both for learning and teaching mathematics. Some ideas to get you started are: 1. Your memories as a student of mathematics  2. Your mathematical strengths and weaknesses your successes and frustrations 3. Any concerns about this class or your future teaching mathematics your philosophy of what mathematics is, how it should be taught, and how it is best learned

Step 1. Open Excel and complete first two columns with any numbers Make 7-8 rows. Type below first column “R = ” We will use Excel function CORREL(Array-1, Array-2). STEP 2. Click on cell B11 and type: =CORREL(x-Array, y-Array)  When you highlight x-array and y-array do not include the title. Press ENTER. You will see in cell B11 Coefficient of Linear Correlation. STEP 3. Analyze the R-value. Does it mean we have strong positive, strong negative, weak correlation or none linear correlation.  STEP 4. Find equation of best fit line for your set of numbers. Equation should be in form:  y = Ax + B where A is a slope and B is y-intercept. To find A and B use Excel functions:  A (slope) = SLOPE(y-array, x-array) B (y-intercept) = INTERCEPT(y-array, x-array) STEP 5. Use your equation of best fit line  to calculate y at any point outside your x-interval.

Respond to the following in a minimum of 175 words:  This week we examine how to solve for an unknown quantity. Some situations may be easily modeled by single variable equations and others might be more difficult. Reflect on your professional or personal world. What is an example of a situation that you might be able to use an equation with a single unknown to help understand? What is an example of a situation that you might not be able to use an equation with a single unknown to understand? What makes an equation with a single unknown helpful in one of your examples but not the other? What patterns exist in your two examples that might be helpful in determining when to use a simple equation?

Your task for this discussion is as follows: Write a system of two linear equations that model something from your daily life. Solve the system of equations in two ways. Discuss which method you liked better and why.

1. Write a short essay related to data privacy. 2. Explain what it means to say, “variables must vary.” 3. List and define the four levels of measurement (nominal, ordinal, interval, and ratio). In your opinion, which one or more is the most appropriate for statistical analysis. Explain. 4. Compare and contrast the characteristics of continuous and discrete variables. What is a common challenge of trying to calculate statistics using discrete variables? 5. Identify the level of measurement for the following examples and explain why you selected the level you did for each: a. Career field (e.g., accountant, production manager, etc.) b. Temperature in Fahrenheit c. A job satisfaction survey measured as “disagree, neutral, agree” d. Total sales for a firm 6. Identify each of the following types of a variable (e.g., continuous versus discrete) and explain why you selected the category you did for each: e. The number of workers in each department of a large organization (e.g., workers in production, sales, accounting, etc.) f. The dollars of revenue earned during a fiscal year g. The number of software licenses available to employees in a firm h. The average annual salary of middle managers of an organization

Understanding descriptive statistics, their measures of center and their variability, helps form the foundation of statistical analysis. Descriptive statistics tell us how frequently an observation occurs, what is considered average, and how far data in our sample deviate from being average. With these statistics, we are able to provide a summary of characteristics from both large and small datasets. Measures of central tendency and variability provide valuable information on their own, and form the cornerstone of the quantitative structures that we build in our research studies. Required Resources Read/review the following resources for this activity: OpenStax Textbook: Chapter 2 Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory business statistics. OpenStax. https://openstax.org/details/books/introductory-business-statistics Lesson Minimum of 1 scholarly source In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s). Initial Post Instructions For this Discussion, you will examine central tendency and variability in terms of pulse rate. Find and record the pulse rate of 10 different people where you work. Tell us a little about the population from which you drew your data. Describe your findings in terms of central tendency and variability. Consider using some of the following to help you form your initial discussion post: What are your measures of central tendency (i.e., mean, median, and mode)? Which might be the better measure for central tendency and why? What is the standard deviation of your data? How variable are the data (range)? Are there any outliers? Investigate possible reasons for these outliers, and things that might limit them if further study were to be carried out. What are some variables that should be considered in discussing your measures of central tendency and variation? Is there any skewness in your measured data? How would you describe this data (i.e. what insights did you gain from this data)?

Z-scores A normal distribution of scores has a standard deviation of ? =10; and a ? = 70. Find the z-scores corresponding to each of the following values: a) A score that is 20 points above the mean. (Hint: what score is 20 points above the mean of ? = 70?) b) A score that is 10 points below the mean. c) A score of x = 50. d) A score of x = 35.

Calculating Confidence Intervals The purpose of this assignment is to practice calculating confidence intervals. For this assignment, students will utilize Excel and SPSS Statistics and the “Example Dataset.” Using the “Example Dataset,” complete the following: Based on a normal distribution curve, calculate the probability of an individual being 60 years or older in this population. Show the Excel and SPSS formulas or your hand calculations. Include screenshots as needed to illustrate this. Using the sample standard deviation of age as an estimate of the population standard deviation, calculate by hand the standard error of the mean. Show your calculations and the answer. Calculate by hand a 95% confidence interval for “Age” based on the sample mean. Use SPSS to verify your answer. Include your calculations and screenshots of the SPSS output. Interpret the confidence interval for age and explain the three pieces of information needed to calculate a confidence interval. Submit one Word document that includes all of the assignment deliverables. APA style is not required, but solid academic writing is expected.