STA3032 Chapter 1

# STA3032 Chapter 1 - Chapter 1 Sampling and Descriptive...

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Chapter 1 Sampling and Descriptive Statistics 1. Introduction: Definition: Statistics is the science of (or a collection of techniques for) Collecting (sampling, census) Classifying (descriptive statistics) Analyzing (e.g., regression analysis) Generalizing (statistical inference) A set of data for a special purpose Each of these activities is based on probability . We will emphasize making inferences about population parameters based on data from random samples. Some new terms need to be defined: Population: a set of well-defined units (objects or outcomes) about which information is sought. Sample: A subset of the population, containing objects or outcomes that are actually observed. Random sample: A sample selected according to some rules of probability Simple Random Sample (SRS): A sample of size n, selected in such a way that every sample of size n (from the population of size N) has an equal chance of being the selected sample. As a result of this property every element in the population has an equal chance (n/N) of being in the random sample. SRS Selected with replacement: Some population units may appear more than once. This is used in theoretical studies. SRS selected without replacement: Any population unit may appear in the sample at most once. This method is used in real life problems. Although the two selection methods are different, the difference becomes negligible when the population size (N) is extremely large, relative to the sample size (n). In this course whenever we talk about a sample we mean a SRS selected with replacement. A SRS selected with replacement gives independent observations, i.e., knowing the value of any one element in the sample does not help in predicting the value of the of he elements. Other sampling methods (such as stratified random sampling, cluster sampling, multi- stage sampling, etc., are used in real-life problems because they are usually ore efficient. In such a case the formulas given in this course need to be modified. Such sampling methods will not be covered in this course. [You may take STA4222 Sampling and Survey Design if you are interested.] STA3032 Chapter 1, Page 1 of 10

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Types of Experiments: One-sample experiment: When there is one population of interest, we select one sample (of n elements) and make inferences about the population parameter(s). Multi-sample Experiment: When we are interested in comparing two or ore populations, we select a random sample from each population and make inferences about the parameters of these populations. Types of Data Quantitative (Numerical) Data obtained as a result of some measurement or counting process of population (or sample) elements. The results can be used in arithmetic operations. Qualitative
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STA3032 Chapter 1 - Chapter 1 Sampling and Descriptive...

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