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Unformatted text preview: 11 Introduction to Statistics 11.1 Introduction 395 11.2 Sampling Theory 396 11.3 Estimation Theory 402 11.4 Hypothesis Testing 411 11.5 Curve Fitting and Linear Regression 418 11.6 Chapter Summary 422 11.7 Problems 422 11.1 Introduction Statistics deals with gathering, classifying, and analyzing data. Statistics is differ- ent from probability. Fully defined probability problems have unique and precise solutions. Statistics is concerned with the relationship between abstract proba- bilistic models and actual physical systems. One of the primary tools of the statis- tician is knowledge of probability theory. A statistician works by postulating a probabilistic model for the system under investigation based on his or her knowledge of the physical mechanisms involved in the system and on personal experience. The statistician expects the model to exhibit a probabilistic behavior that is similar to that of the physical system. There are two general branches of statistics: descriptive statistics and induc- tive statistics (or statistical inference ). Descriptive statistics deals with collecting, grouping, and presenting data in a way that can be easily understood. It is con- cerned with issues such as summarizing the available data by such variables as the mean; median (or the middle data value when the data values are ordered in size from the smallest value to the largest value); mode (or the value that occurs 395 396 Chapter 11 Introduction to Statistics most frequently); and measures of the spread of the data, including range, vari- ance, and standard deviation. It can also describe the data by a set of graphs, bar charts, tables, and frequency distributions. Statistical inference uses the data to draw conclusions (or inferences) about, or estimate parameters of, the environment from which the data came. That is, statistical inference is concerned with making generalizations based on a set of data by going beyond information contained in the set. There are different aspects of inductive statistics, which we will consider in the remainder of this chapter. These include the following: 1. Sampling theory , which deals with problems associated with selecting samples from some collection that is too large to be examined completely. 2. Estimation theory , which is concerned with making some prediction or esti- mate based on the available data. 3. Hypothesis testing , which attempts to choose one model from several postu- lated (or hypothesized) models of the physical system. 4. Curve fitting and regression , which attempts to find mathematical expressions that best represent the collected data. 11.2 Sampling Theory In statistics, the collection of data to be studied is called a population . A popula- tion can be finite or infinite. For example, a study on the number of students in the electrical engineering department of a college deals with a finite population....
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