An Introduction to Business Statistics

1. An Introduction to Business Statistics

2. Let’s say I am interested in every person who is in the city limits of Wayne, Nebraska at the point in time August 20, 2012 at 12:30pm. Just for kicks, let’s imagine at this time that every person in the city limits at this time is frozen in place. It would be like freezing the video of a movie at a particular frame. Let’s say then that you and I can walk around while all the rest of the folks in town are frozen in place. But, when we get to a person we can talk to them. Say we ask each personwhat was their income in 2011, what was their age on August, 2012, how much do they like Coca Cola (and the person has to answer either “hate it,” “its okay,”, or “I love it.”), what continent would you like to live on in 2013 (and you have to say 1 of the 9 ;).

3. Data As we talk to each person we could record their responses. We would probably want to be organized, so let’s use the following (note each row represents measurements on the each person and each colum is variable): PersonIncome AgeCoke Continent Person 1 23,750 22Love it North America Person 2 72,800 54 Hate itAsia Person 335,432 36 Hate it North America Person 4 10,000 29its okay Europe We would have data on more people when we are done because probably more than 4 people are in Wayne at this time.

4. Population Often in statistics we are interested in a group. The group may be large, or even huge! Plus we want to be able to make statements or draw conclusions about the group. A population is the set of all elements we want to study or know something about. So, the population is the main group we want to know about or draw conclusions about. A census is conducted if we have measurements on all the elements in a population. Note in our class a population may not be about people. For example, we might be interested in every bottle of Mt. Dew produced at a local bottling company.

5. Sample Many times in a study all the elements of the population will not be observed, so a subset of the population, called a sample, is said to have been taken. A sample is a subset of the elements of a population – just part of the population.

6. Descriptive Statistics Describing data is a big part of statistics. A fair amount of time will be spent in this class describing data by calculating measures such as the mean and the standard deviation and we might use tables and graphs to assist in learning about the elements of the study. Descriptive statistics deals with methods of organizing, summarizing, and presenting data in a convenient and informative way.

7. The Mean You may recall from your prior school daze the concept called the average. Maybe you had 3 tests and so the average test score would be found by adding the 3 scores and dividing the result by 3. In a stats class we usually call the average the mean! The mean is an example of a numerical descriptive measure. A parameter is a descriptive measure of a population and the mean is an example of parameter. A statistic is a descriptive measure of a sample and the mean is an example of a statistic.

8. Parameters and Statistics So, parameters refer to populations and statistics refer to samples. The population mean is a parameter and the sample mean is a statistic. Often we just say mean and the interpretation about it being a parameter or statistic depends on the context of having either a population or a statistic. Later we will be introduced to other descriptive measures.

9. Inferential Statistics Inferential Statistics is a method used when only a sample from a population has been drawn, but we want to make statements about the important aspects of the larger population. Any cooks reading this? In order to tell if a pot of soup is ready to go, is taking a sample okay? Sure it is, but first make sure you have stirred the soup to mix in the ingredients. In statistics, we feel pretty good about samples as long as we have “mixed” things well.

10. Examples Say we want to study faculty salaries at WSC. Our research topic is faculty salaries. The population is WSC faculty. Elements are individual faculty. Parker is an element of the population, as is Lutt, Paxton, Nelson, and others. Another example might be we want to study the budgets of state governments. The population is all 50 states. The elements are the states. What are the elements? (Did you say something like Ohio, Nebraska, Iowa….?) Our interest may be people, companies, states, etc…

11. Statistical Inference I mentioned a few slides back that inference is about using a sample to make a statement about a population. More formally, inference is the process of making an estimate, prediction, or decision about a population based on a sample of data. Often it is time consuming, impractical and expensive to look at every member of the population. That is why a sample is drawn. Because only a sample is drawn, sometimes the estimate, prediction, or decision made about the population based on the sample will be WRONG. Does this seem weird to you? For now interpret this as the resulting sample isn’t giving an accurate reading of the population.

12. Confidence level and significance level The confidence level is the proportion of times that an estimating procedure will be correct. The significance level measures how frequently the conclusion about a population will be wrong in the long run. WHAT IS GOING ON HERE? The only way we know for sure about a population is to look at all the members of the population. But this is time consuming! So we have a trade-off – cost for accuracy! So, when we take a sample, we have measures to help us assess how “good” are conclusions are likely to be. Would you be okay with a confidence level of 95%? What would you say about a level of significance of 5%?

13. A note on data and our class During the term you will work on many problems in the book (hopefully more than just the ones I assign). You can assume the data in the problem has been collected properly. As you work a problem focus your attention on the concepts in the chapter and try not to get lost in the application to which the problem refers.