Chapter 1 2114

Chapter 1 2114 - WelcometoENGR20:...

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Welcome to ENGR 20:  Probability and Statistics for  Engineers I 1
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Chapter 1 2
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3 Problem to which Descriptive Statistics can be applied: Which machine to purchase? You are a manufacturing engineer. Two machines, both able to produce a washer that you need for one of the major components in your product line, are available to purchase from two different vendors. These machines are very expensive and it is critical to your product that the diameter of each washer be within specifications. You were able to run a small sample on each machine and the resulting diameter of each washer is shown below (in mm). Washer Machine 1 Machine 2 1 2.13 1.95 2 2.22 2.05 3 1.95 2.08 4 1.99 1.92 5 1.98 1.96 6 2.06 1.98 7 2.08 2.01 8 2.11 2.01 9 2.06 2.03 10 2.07 1.99 If the specifications call for diameters of 2.0 ± .05 mm which machine are you going to recommend? Why?
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Definitions of “Statistics” 4 The collection, organization, analysis, interpretation, and presentation of data. Statistics allows for the extraction of information from data to make inferences. The branch of scientific inquiry that provides methods for organizing and summarizing data and for using information in the data to draw various conclusions. The analysis of numerical data for the purpose of reaching a decision or communicating information in the face of uncertainty.
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Populations and Samples A population consists of all individuals or objects of a particular type. A numerical population is the set representing all measurements of interest to an experimenter. If the measurement is a two-valued type (an opinion poll, for example) the population is called a dichotomous population . Sometimes in a particular statistics problem, we may have a conceptual or hypothetical population in which the population consists of all possible measurements that might be made under certain conditions. A sample is a subset of measurements selected from the population of interest (Examples - Simple random sample; Systematic random sample ; Stratified sample; Convenience sample). 5
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What This Course Covers Descriptive Statistics - consists of procedures used to organize and summarize (or describe) the important characteristics of a set of measurements. A descriptive statistics with which you are probably familiar is the mean. Probability - forms a bridge between descriptive and inferential statistics and gives us an understanding of the properties of a population based on its distribution. Probability helps us to understand if certain outcomes are likely given certain conditions. Probability reasons from the population to the sample - this is known as deductive reasoning. Inferential Statistics - allows us to draw conclusions about populations based on information contained in a sample. This is the main focus of the book and this course. As engineers, we often need to be able to draw conclusions about populations based on samples. Statistics reasons from the sample to the population - this is known as inductive reasoning.
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Chapter 1 2114 - WelcometoENGR20:...

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