Chapter 7 Sampling and Sampling Distributions

Chapter 7 Sampling and Sampling Distributions - Chapter 7...

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Chapter 7 – Sampling and Sampling Distributions Simple Random Sampling - The meaning of a simple random sample and the process of selecting a simple random sample depends on whether the population is finite or infinite Sampling from a Finite Population - A simple random sample size of n from a finite population of size N is a sample selected such that each possible sample of size n has the same probability of being selected - When a sample being selected excludes previously used random numbers, this is sampling without replacement . If on the other hand a sample was selected in a way such that previously used random numbers and specific values could be included in the sample two or more times, this is sampling with replacement Sampling from an Infinite Population - A simple random sample from an infinite population is a sample selected such that the following conditions are satisfied: 1. Each element selected comes from the population 2. Each element is selected independently - The purpose of each element being selected independently is to prevent selection bias - Infinite populations are often associated with an ongoing process that operates continuously over time Point Estimation - To estimate the value of a population parameter, a corresponding characteristic of the sample is computed, called the sample statistic - For example, to estimate the population mean μ and the population standard deviation σ , the data is used to calculate the corresponding sample statistics: the sample mean xbar and the sample standard deviation s - By making these computations, the statistical procedure of point estimation is being done. The sample mean xbar is the point estimator or the population mean μ, and the sample standard deviation s is the point estimator the population standard deviation σ - The point estimates differ somewhat from the corresponding population parameters (the difference is to be expected because a sample is being used to develop the point estimates, rather than a census of the entire population) Introduction to Sampling Distribution - If another sample was taken of the same population, different point estimators are likely to result - When the process of selecting a simple random sample is considered as an experiment, the sample mean xbar is the numerical description of the outcome of the experiment. Because the various possible values of xbar are the result of different simple random samples, the probability distribution of xbar is called the sampling distribution of xbar - The sampling distribution and its properties allow for probability statements to be made about how close the sample mean is to the population mean - From the approximation, the distribution appears to be bell-shaped
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