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Unformatted text preview: What is statistics? • Statistics is the science of learning from data . It uses the theory of probability to make inferences about populations or processes using data • For example, we would like to know the mean of a characteristic of a set of elements of a population • But we can’t observe or measure each one because there are too many elements or not all are available. 1 Examples • Mean blood pressure of 40 year old pregnant females. • Mean lifetime of 60watt bulbs being made at the G.E. plant in Cleveland. • Mean potency of an antibiotic after storage for 20 months on store shelves. 2 Population versus Sample Since we can’t obtain the average exactly, we do the next best thing • approximate it by finding the average for a selected subset of the elements • we do a statistical study to estimate the population mean • usually, there are many objectives of a statistical study , than just estimating the mean of the population. 3 Steps in a Statistical Study • Collecting data by making observations or taking measurements on some sample or process of interest, possibly as a part of a statistically designed experiment or a survey. • Summarizing the data using statistical summary methods (calculating means or constructing a histogram, for example). • Analyzing the data and making inferences using models and statistical methods for drawing conclusions about the situation being considered. 4 Terminology and definitions • Population The set of all objects (or measurements) of interest; they are called elements of the population. • Sample Any subset of elements from a population. • A statistical study is made using a sample obtained from a population. 5 How to Select a Sample? Theoretically we can get a random sample of n elements by • making n draws, one at a time • on each draw, each remaining element in the population is equally likely to be the one drawn. Practically we can seldom satisfy the theoretical requirements, so we do the best we can to introduce randomness into our sample selection process. 6 How to Select a Sample? (continued) Can the result of a statistical study of population mean (average) be far away from the true mean?  sure, sometimes. A statistical study provides evidence. It doesn’t prove anything A random sample selected using the method described earlier ensures that each sample of size n drawn from a population has the same chance of being selected Methods that ensure this property are called simple random sampling We shall use a method for selecting a simple random sample from a population in a one of our labs using random digit tables 7 Data Description Two broad applications of Statistics • descriptive statistics • inferential statistics When measurements from an entire population is available to us data description will be a major objective....
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This note was uploaded on 01/23/2010 for the course STAT 213 taught by Professor Hao during the Spring '10 term at Internet2.
 Spring '10
 hao
 Statistics, Probability

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