stat 401 homework solutions

stat 401 homework solutions

Statistical Analysis in STAT 401

1. Introduction to STAT 401

Stat 401 is a chance for students of economics to equip themselves with the required skills to process and analyze information using the statistical software Stata and Microsoft Excel. Today, more than ever, managers and decision-makers in every branch of the economy have to rely on computerized algorithms to turn the vast amount of raw data – which accumulates day by day – into valuable information. And this is particularly true when it comes to the modern medical laboratory, as well as clinical and epidemiological research. Consequently, the demand for professionals who have a strong command of these sought-after skills is ever increasing. Professor X begins his introduction with the words: “Welcome to Stat 401.” He then gives an overview of the course, the textbooks, the grading policy, and the homework sessions. The course aims “to provide an education in the basics of modern applied statistics.” Professor X makes clear that the focus of the course will be on the capacity and practical use of these statistical methods in social and economic research, which means students will spend most of their time learning how to apply these methods to real data. In addition to these, he also introduces the required technology including the computer services, the statistical and graphical software. He emphasizes that in order to benefit the most from this course, students are expected to initiate activity themselves and not to be passive in class. In terms of his teaching methodology, Professor X explains that, “I will generally introduce the definition of a method but then quickly illustrate and spend the vast majority of the lecture doing the examples.” He also highlights the three midterms and the final as well as clarifying the content of the exams and the material covered for each. He also mentions how he weights the midterms against the final and draws students’ attention to the final’s character as a cumulative exam.

2. Descriptive Statistics

The next chapter of our work, “2. Descriptive Statistics,” focuses on organizing and summarizing data. The basic ways of looking at data and summarizing data are covered. Different types of data, such as quantitative or qualitative, are also discussed. This chapter is important in that it serves as a foundation for introducing several key concepts and tools that are critical to carrying out statistical analyses. Quantitative and qualitative data are introduced early in this chapter. These are two broad types of data. Quantitative data are always numbers and represent a measurement. On the other hand, qualitative data take non-numeric values and describe “what” is depicted. Enriched with examples and a well-organized structure, many concepts and terms in descriptive statistics are introduced in a clear manner. For example, the formula for calculating variance and standard deviation and the meaning for interquartile range are all explained in an intuitive way through the work. I believe students will have no problem in following the logic and the formulas in this way. The part of graphical representation of data is also useful to students who have had no exposure to the corresponding discipline before. In addition, the chapter also introduces to students the basic graphic forms in summarizing data, such as bar chart, pie chart, and stem-and-leaf display. It also explains how to determine the symmetry of a graph. These materials provide a hands-on experience on Excel. There are step-by-step instructions for using Excel to obtain the sample mean and sample standard deviation, etc. It allows students to do the calculations with the help of computer and hence to concentrate more on understanding the results. The chapter concludes with two real life examples, namely the Canadian lynx data and Roundup effect on earthworms. This gives students a flavor of what they will be expecting in the study of inferential statistics, which is covered afterwards in the work.

3. Inferential Statistics

Inferential statistics uses sample statistics to make estimates about the parameter of a population. The goal is to draw valid conclusions about various parameters of a population. There are different methods and techniques for inferential statistics, and this section of the STAT 401 material provides an overview of these methods. One of the fundamental principles is probability and that is where the journey of inferential statistics begins. By understanding probability, we can investigate how likely certain events are and that is very important when we draw conclusions about a population from a sample. Random variables, which can be thought of as different outcomes that can result from an experiment, are introduced. The concept of distribution of a random variable is then discussed. The concept of standard error is introduced before we dive into the core component of inferential statistics: confidence intervals. The section concludes with the difference between an observational study and an experiment, and that enables us to introduce ‘Confounder’, a term that is regularly used in medical statistics when discussing results from different studies. I feel this section not only clearly introduces and investigates each topic, but also provides an overview of the whole journey of inferential statistics from probability. Also, all the key terms are explained and illustrated with examples, which is very useful for quick recaps later.

4. Hypothesis Testing

If we observe a sample data that holds a certain kind of “hypothesized” property, then at any point in the future, we can make an independent conclusion against the truth of that hypothesis. This is the main philosophy of statistical hypothesis testing. We start this section with the conceptual ideas of the null hypothesis. The null hypothesis, denoted by H0, is the hypothesis that the sample data comes from a population that holds a certain property. We can almost formalize the null hypothesis in the opposite way. Most of the time, you end up explaining what the alternative hypothesis is, which is denoted by Ha. The alternative hypothesis is just a statement of what the sample data is being suspected for. Always make sure that if you are comparing one group with another group, the null hypothesis should be seen as a statement of no effect or no difference. For example, if we want to check the effectiveness of a medicine, then the null hypothesis will be seen as a statement indicating that the medicine has no effect. Before we perform any statistical test and eventually make decisions, several steps should be followed, and we should strictly obey the criteria of those steps. Here we cover the logic of hypothesis testing, choosing an appropriate test statistic, decision-making processes based on p-value, and we also talk about type I and type II errors and their respects. We also discuss some of the most applied and widely used tests in practice as examples, such as the z-test, the t-test, and the Chi-Square test.

5. Conclusion and Homework Solutions

First, the course has provided an impression to the students on the importance of statistics in analyzing data. It also provides a basic understanding of the application of statistics in real-life situations. Then, we have gone through the descriptive statistics. Descriptive statistics is about summarizing and presenting data. Graphical and numerical methods are commonly used in descriptive statistics. We have gone through a few graphical methods such as histogram, boxplot, stem and leaf plot, and etc. On the other hand, we have learned how to use R to produce those graphs. Next, we have the inferential statistics. Inferential statistics is about making inferences and drawing conclusions based on a sample. The other aspect of inferential statistics that we have learned in the class is about estimation. We have learned how to obtain a point estimate and also an interval estimate. Hypothesis testing is then discussed, which involves making decisions. When we are doing hypothesis testing, we have to make a decision about the population based on sample data. We have gone through the steps in hypothesis testing, the types of hypotheses, and the comparison between the P-Value method and the critical value method. Population proportion, population mean, and the differences in population means are the three types of hypothesis testing using the normal distribution that we have discussed in the class. The chi-square distribution is being introduced. The chi-square distribution is associated with hypothesis testing. Besides that, we have learned about the chi-square test for goodness of fit and also the chi-square test for independence. After the tests that we have gone through, the course has provided the methods or the way to present the results obtained from the statistical data and testing. Last but not least, the course has provided t…