chapter7 - Introduction to Probability and Statistics...

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1 Introduction to Probability and Statistics Thirteenth Edition Chapter 7 Sampling Distributions Introduction • Parameters are numerical descriptive measures for populations. – For the normal distribution, the location and shape are described by m and s . – For a binomial distribution consisting of n trials, the location and shape are determined by p . • Often the values of parameters that specify the exact form of a distribution are unknown. • You must rely on the sample to learn about these parameters. Sampling Examples: • A pollster is sure that the responses to his “agree/disagree” question will follow a binomial distribution, but p , the proportion of those who “agree” in the population, is unknown. • An agronomist believes that the yield per acre of a variety of wheat is approximately normally distributed, but the mean m and the standard deviation s of the yields are unknown. If you want the sample to provide reliable information about the population, you must select your sample in a certain way! Simple Random Sampling • The sampling plan or experimental design determines the amount of information you can extract, and often allows you to measure the reliability of your inference . Simple random sampling is a method of sampling that allows each possible sample of size n an equal probability of being selected. Example •There are 89 students in a statistics class. The instructor wants to choose 5 students to form a project group. How should he proceed? 1. Give each student a number from 01 to 89. 2. Choose 5 pairs of random digits from the random number table. 3. If a number between 90 and 00 is chosen, choose another number. 4. The five students with those numbers form the group. Types of Samples • Sampling can occur in two types of practical situations: 1. Observational studies: The data existed before you decided to study it. Watch out for Nonresponse: Are the responses biased because only opinionated people responded? Undercoverage: Are certain segments of the population systematically excluded? Wording bias: The question may be too complicated or poorly worded.
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2 Types of Samples • Sampling can occur in two types of practical situations: 2. Experimentation: The data are generated by imposing an experimental condition or treatment on the experimental units. Hypothetical populations can make random sampling difficult if not impossible. Samples must sometimes be chosen so that the experimenter believes they are representative of the whole population. Samples must behave like random samples! Other Sampling Plans • There are several other sampling plans that still involve randomization : 1. Stratified random sample: Divide the population into subpopulations or strata and select a simple random sample from each strata.
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chapter7 - Introduction to Probability and Statistics...

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