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Ch 1 Notes

# Ch 1 Notes - 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 entities that we learn about—people, animals, objects, states, spins of a roulette wheel—are called subjects . Populations and Samples The group of all subjects of interest is called the population . Any of the following could be a population: all UF psychology majors all Delta domestic flights in 2007 all possible flips of the quarter in my pocket Notice that a population can sometimes be something abstract, like “all possible” of something.

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1.1 Fundamental Ideas 2 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: 18 UF psychology majors, randomly chosen by UFID 40 Delta domestic flights, randomly chosen by flight number 100 flips of the quarter in my pocket Random Sampling The idea of sampling is that the characteristics of our sample should probably 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. 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. A parameter is a number that summarizes a population, like the popu- lation mean. Since we usually don’t have data for the entire population, population parameters are usually unknown. A statistic is a number that summarizes a sample, like the sample mean. Since we have data for all subjects in the sample, we always know the value of a statistic. Example 1.1 : The average price of gas today in all Florida gas stations, which we almost certainly don’t know, is a parameter. The average price of gas today at eight randomly selected Florida gas stations is a statistic, and we could easily calculate it once we actually take the sample. Estimation The key idea is that, as long as our sample is fairly representative of the population, we can use (known) sample statistics to estimate (unknown)
1.2 Collecting and Describing Data 3 population parameters. If the average price of gas at the eight stations in the sample is \$ 3.81, then it’s reasonable to estimate the average price of gas statewide is around \$ 3.81, but not necessarily \$ 3.81 exactly. We’ll develop this idea a lot more later.

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