[MUSIC] Hello, everyone and welcome to the fourth lecture of the statistics for international business mooc. This week, introduces you to the concept of estimation. Statistical analysis requires that we obtain a sample from a population of units that are of interest and have particular characteristics. If we do not have a properly constructed sample, then all the methods we have been discussing will not be working correctly. Therefore, we must first learn how to obtain a sample. Sample observations can be shown to the random variables. That is they are appropriately chosen. Statistics, such as the sample mean or the proportion computed using sample observations are also themselves random variables. Using our understanding of random variables from week three of our course, we can make probability statements about the sample statistics computed from our sample and then make inferences about the populations from which the samples were obtained. All of this leads to some important and very powerful results. But first, we need to have probability distributions for the sample statistics. That is the first part of the analysis during this week. After we complete that, we move on and address situations that require an estimate of a population parameter. Inferential statements concern the estimates of a population parameter based on information that a random sample contains. More specifically, we discuss procedures to estimate the mean of population. A proportion of population members that possess some specific characteristic and then the variance of the population. We will present two estimation procedures. We'll begin first, by estimating an unknown population parameter by a single number. This is called a point estimates. However, for most real world problems, the point estimate on its own is not adequate. A more complete understanding of the process that generated the population requires that we obtain a measure of variability. Therefore, to achieve that, we discuss a procedure that takes into account this variation. To do this, we construct an interval of values. This is called a confidence interval. It is likely to include the quantity, the parameter of interest. The second part of this week is going to introduce you to the concept of hypothesis testing. In this part, we will introduce a framework that is general enough to test all sorts of hypothesis. First, we have to define the two possibilities, the two alternatives if you wish that cover all possible outcomes. Then by using statistics computed from the random sample, we'll pick one of the two alternatives under consideration. Because these statistics we are constructing are drawn from a sampling distribution, the decision we make has some randomness in it, obviously. Thus, clear decision rules are needed for choosing between the two alternatives. Sample statistics cannot in general be used to prove in an absolute sense that one or the other of the two alternatives is the correct one. However, we can find that one of the alternatives has a small chance, a small probability of being the correct one. As a result, we will go on to select the other alternative. Now, this approach is a fundamental process of decision-making and is used throughout fields involving scientific research. Now, a good way of explaining this process is to think of it like a jury trial. I mean, this example is pointed out by Paul Newbold and William Carson is their book statistics for business and economics. To quote them, the process that we develop here have a direct analogy to criminal jury trial. A person who is charged with a crime is either innocent or guilty. In a jury trial, we assume that the accused is innocent initially and then the jury will decide that the person is guilty only if there is very strong evidence against the presumption of innocence. That is the jury would reject the initial assumption of innocence. The criminal jury trial process for choosing between guilt and innocence has the following characteristic. First, there are rigorous procedures or rules for presenting and evaluating evidence. Second, a judge is there to enforce the rules. Third, a decision process assumes innocence, unless there is evidence to prove guilt beyond reasonable doubt. Note that this process will fail to convict some people who are in fact, guilty. But if a person's innocence is rejected and the person is then found guilty, we do have strong evidence that this is the case, that the person is guilty. Now during the last part of the week, the third part, we will introduce the concept of regression analysis. Regression analysis analyzes the dependence of one variable which we call the dependent valuable on one or more other variables and these are called the explanatory variables, or the independent variables. The aim here is to estimate average value or the mean of the former of the dependent variable in the population in terms of the fixed values of the independent or exogenous variables. The regression concept can be represented by a function that can be either linear or nonlinear. Our focus is on linear single equation regression models where one variable, the dependent one as we've been saying is a linear function of some other explanatory variables. Now these models implicitly assume that there are some causal relationships possibly, if any between the dependent and the explanatory variables and that relationship goes in one direction from the explanatory variables to the dependent variable. Regression procedures have a wide range of applications, such applications include a number in business, finance and economics. Thank you very much. [MUSIC]