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chapter1 - Statistics 630 1 Introduction What is statistics...

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Statistics 630 1 Introduction What is statistics? Statistics is a science that quantifies the uncertainty inherent in conclusions drawn from less than complete information. The mathematical theory of probability is the main tool used in quantifying uncertainty. Examples of statistical problems: A prescribed amount of a hormone is administered to a mouse. Does this affect the expression of a particular gene in the mouse’s genome? If 450 people out of 1000 in a survey say they want more gun control, what can we say about the percentage of all people who want more gun control? Chapter 1: Introduction to Probability Copyright c 2009 by Thomas E. Wehrly Slide 1
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Statistics 630 In the last problem, here’s an example of a conclusion stated in statistical terms: One may be 95% confident that the percentage of all U.S. adults who favor more gun control is between 42% and 48%. Two main components of the statistical paradigm: Population Sample The population is a collection of numbers about which one wants to draw a conclusion or make an inference . The sample is a subset of the population. Chapter 1: Introduction to Probability Copyright c 2009 by Thomas E. Wehrly Slide 2
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Statistics 630 The problem of interest: Draw a conclusion about the population based on information in a sample. Typically, the population is so large that it is too time-consuming and/or expensive to determine every number in the population. So, we look at just a subset of the population, and usually a relatively small subset. For example, there are more than 100 million adults in the US, but a survey may only consider 1000 of them to estimate the proportion having a given opinion. 1000 100 , 000 , 000 × 100% = 0 . 001% Somewhat surprisingly, if it is obtained in a prescribed way, a sample containing less than one thousandth of a percent of the population can actually provide very accurate results about the entire population. Chapter 1: Introduction to Probability Copyright c 2009 by Thomas E. Wehrly Slide 3
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Statistics 630 Conclusions (about a population) based on information in a sample are marked by uncertainty, at least when the sample is a proper subset of the population. Such conclusions are called inductive . Induction – Reasoning from specific to general Deduction – Reasoning from general to specific In our statistical paradigm: sample ⇐⇒ specific population ⇐⇒ general Probability is the tool used in quantifying the uncertainty in inductive statistical conclusions. Chapter 1: Introduction to Probability Copyright c 2009 by Thomas E. Wehrly Slide 4
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Statistics 630 2 Experiments and Events So, we now begin our study of probability. One can make the study of probability completely abstract, just as with any other mathematical discipline. Instead, I will try to use examples that show how probability is used in statistics.
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