# MAth 279 Statitics booklet

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Engineering Statistics Math 279 Supplemental informative Booklet This Booklet is intended to be used as a supplement to the engineering statistics Text Book used at the time the course is taken. It contains definitions and supplemental exercises that are intended to enhance mastery of topics taught in the course. This booklet is not intended to replace the Text Book. Name: _____________________ Course:_______ Section: ______ 1
1.1 Essential Definitions and Vocabulary Statistics : A collection of methods used for planning experiment, obtaining data and then analyzing interpreting and drawing conclusions based on that data. Deductive reasoning : Reasoning based on previous conclusions and assumptions and passed experiences and generalizations. Example : A certain patented detergent used in gasoline contributes to cleaner burning power in combustion engines, thus better gas millage. All gasoline brands using such detergent are expected to contribute to better gas millage. Inductive reasoning : Reasoning based on inferences and generalization that may or may not be substantiated by real life experiences. Statistics is often inductive in nature since the inferences are basically generalizations and may or may not correspond to reality. Example : Certain size block of wood used in construction of some old bridges and pathways are expected to show fatigues after a certain amount of force per square foot. There are bridges in existence that are still operational enduring forces way beyond the recommended levels. Descriptive statistics : Techniques of interpreting, analyzing and drawing conclusions from descriptive means such as graphs, tables and charts. Inferential Statistics : Techniques of interpreting the values resulting from descriptive techniques and making inference about a population. Most important topics of inferential statistics are: 1) Estimation: Planning a budget for a major city . 2) Hypothesis testing: a claim is drawn against a product and its reliability. 3) Correlation and Regression : The ranking of two applicants. The Engineering method and Statistical thinking The engineering or scientific method of formulating and solving a problem. - Develop a clear description of the problem - Identify the factors that effect the problem - Propose a model for the problem using scientific & engineering knowledge - Collect data through experimentation - Refine the model base on observed data - Work with the model to assist in finding the solution - More experimentation base on the manipulated model - Draw conclusion and make recommendation based on the solution. 2
Population : A collection or set of individuals, scores, items, objects or items to be analyzed. Conceptual Population: Population studied after specific measures were tested and used to create the population. After examining certain type of steel beam in a construction project, samples of the same beam were subjected to other treatments to increase the strength and durability. Sample : A subset of population. A smaller group of population members picked from the population. In most engineering statistical studies, a random sample is mostly used for the method to work correctly. Variable : A characteristic of interest about each individual element of population. In a study of f braking points of shear pins the breaking point is the variable. Range of variables : Associating numerical values with a variable is called the range of variables. Assuming a study is being done on the heights of 250 shear pins and their breaking points to disengage a machinery. If no other categories or properties used and each pin is identified with a number from 1-250. Analytical study : a study or and experiment where the conclusions are to be drawn relative to a future population . Enumerative Study : a study about a sample used to make a conclusion about the population that the sample was drawn from. Data : The value of variables associated with members of population or sample. Data is almost always the sample picked from the population. Example : Breaking points of shear pins used to break in order to disengage a heavy machinery system and preventing it from further damage to the machinery. Experiment : A planned activity whose results yield a set of data. Example : 100 shear pins are used and subjected to forces beyond the manufacturer's recommended standards. The number of attempts and the results are recorded to determine an average breaking points. Subjecting the shear pins to higher forces than recommended is the experiment. Parameter : A numerical value describing some characteristic of population. Statistic : A numerical value describing some characteristic of sample. 3