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Chapter 1:

Chapter 1:. Sampling and Descriptive Statistics. Why Statistics?. Uncertainty in repeated scientific measurements Drawing conclusions from data Designing valid experiments and draw reliable conclusions. Section 1.1: Sampling. Definitions:

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Chapter 1:

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  1. Chapter 1: Sampling and Descriptive Statistics

  2. Why Statistics? • Uncertainty in repeated scientific measurements • Drawing conclusions from data • Designing valid experiments and draw reliable conclusions

  3. 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.

  4. Simple Random Sampling • A SRS is not guaranteed to reflect the population perfectly. • SRS’s 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.

  5. 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. More on SRS

  6. 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. SRS (cont.)

  7. Types of Data • Numerical or quantitative if a numerical quantity is assigned to each item in the sample. • Height • Weight • Age • Categorical or qualitativeif the sample items are placed into categories. • Gender • Hair color • Zip code

  8. Section 1.2: Summary Statistics • Sample Mean: • Sample Variance: • Sample standard deviation is the square root of the sample variance. • If X1, …, Xnis a sample, and Yi = a + b Xi ,where a and b are constants, then • If X1, …, Xnis a sample, and Yi = a + b Xi ,where a and b are constants, then Segue…

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