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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl Chapter 1: Sampling and Descriptive Statistics

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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl Why Statistics? Uncertainty in repeated scientific measurements Drawing conclusions from data Designing valid experiments and draw reliable conclusions

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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl Section 1.1: Sampling Definitions: A population is the entire collection of objects or outcomes about which information is sought. A sample is a subset of a population, containing the objects or outcomes that are actually observed. A simple random sample (SRS) of size n is a sample chosen by a method in which each collection of n population items is equally likely to comprise the sample, just as in the lottery.

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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl Simple Random Sampling A SRS is not guaranteed to reflect the population perfectly. SRSs always differ in some ways from each other, occasionally a sample is substantially different from the population. Two different samples from the same population will vary from each other as well. This phenomenon is known as sampling variation.

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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl More on SRS Definition: A conceptual population consists of all the values that might possibly have been observed. For example, a geologist weighs a rock several times on a sensitive scale. Each time, the scale gives a slightly different reading. Here the population is conceptual. It consists of all the readings that the scale could in principle produce.

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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl SRS (cont.) The items in a sample are independent if knowing the values of some of the items does not help to predict the values of the others. Items in a simple random sample may be treated as independent in most cases encountered in practice. The exception occurs when the population is finite and the sample comprises a substantial fraction (more than 5%) of the population.

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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl Types of Data Numerical or quantitative if a numerical quantity is assigned to each item in the sample. Height Weight Age Categorical or qualitative if the sample items are placed into categories. Gender Hair color Zip code

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Statistica per lingegneria e le scienze William Navidi Copyright © 2006 – The McGraw-Hill Companies srl Section 1.2: Summary Statistics Sample Mean: Sample Variance: Sample standard deviation is the square root of the sample variance. If X 1, …, X n is a sample, and Y i = a + b X i,where a and b are constants, then Segue…

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