chapter01_mine - Chapter 1 Basic Concepts First well review...

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Chapter 1 Basic Concepts First we’ll review some ideas that you should have seen in your first course in statistics. You should have learned a lot more in that course than just what we’ll cover in this chapter, because we’re only going to address the specific concepts that you’ll need to understand to be successful in this course. The material in this chapter corresponds to Chapters 1–2 and 4–7 of the textbook. 1.1 Fundamental Ideas The purpose of statistics is simply to learn something from data. The enti- ties that we learn about—people, animals, objects, states, spins of a roulette wheel—are called subjects . You should understand however that most pro- cedures used in statistics are based on certain assumptions. That means that while using those procedures you implicitly assume that assumptions hold or at least our populations behaves close to our assumptions. We will not specify all the assumptions rigorously in this course but you should be aware that they are required. Z Populations and Samples The group of all subjects of interest is called the population . Any of the following could be a population: ˆ all UF psychology majors
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1.1 Fundamental Ideas 2 ˆ all Delta domestic flights in 2007 ˆ all possible flips of the quarter in my pocket ˆ United States population Notice that a population can sometimes be something abstract, like “all possible” of something. Ideally, we would like to have data for the entire population . If that’s not possible or feasible, then we try to collect data for a sample of the population. A sample might be any of the following: ˆ 18 UF psychology majors, randomly chosen by UFID ˆ 40 Delta domestic flights, randomly chosen by flight number ˆ 100 flips of the quarter in my pocket ˆ 10000 individuals randomly selected across all 50 states based on their address, social security number etc Random Sampling The idea of sampling is that the characteristics of our sample should prob- ably be similar to the characteristics of the whole population. The best way to ensure this is to choose subjects from the population using a truly random procedure , like drawing names out of a hat, or more commonly, using random numbers generated by a computer. The result is a random sample . Z Parameters and Statistics Often we want to use numbers to summarize a group of subjects. What we call those numbers depends on the group we’re summarizing. ˆ A parameter is a number that summarizes a population, like the pop- ulation mean usually denoted by μ . Since we usually don’t have data for the entire population, population parameters are usually unknown.
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1.1 Fundamental Ideas 3 ˆ A statistic is a number that summarizes a sample, like the sample mean usually denoted by ¯ X . Since we have data for all subjects in the sample, we always know the value of a statistic. Statistics depends only upon the data in the sample and is free of unknown parameters. Example 1.1: The average price of gas today in all Florida gas stations,
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chapter01_mine - Chapter 1 Basic Concepts First well review...

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