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Sampling Methods and Central Limit Theorem

This chapter covers the importance of sampling in statistical analysis, different sampling methods, and the application of the Central Limit Theorem. Topics include simple random sampling, systematic random sampling, stratified random sampling, and cluster sampling.

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Sampling Methods and Central Limit Theorem

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  1. Basic Statistics for Business and Economics Fifth Edition Chapter 8 Sampling Methods and the Central Limit Theorem Douglas William Samuel Irwin/McGraw-Hill

  2. Topics Covered • Why a sample? • Sampling Methods • Sampling Distribution

  3. Sampling Methods and the Central Limit Theorem • Why a sample? A sample is a portion or part of the population Of interest. In many cases, sampling is more feasible than studying the entire population.

  4. Sampling Methods and the Central Limit Theorem Reasons to Sample - The time-consuming aspect of contacting the whole population. • The cost of studying all the items in a population • The adequacy of sample results in most cases.

  5. Sampling Methods and the Central Limit Theorem Sampling Methods 1- Simple Random Sampling 2- Systematic Random sampling 3- Stratified random sampling 4- Cluster Sampling

  6. Sampling Methods and the Central Limit Theorem 1- Simple Random Sampling A sample selected so that each item or person in the population has the same chance of being included. • Use a starting point in the table., any starting point will do. • Suppose a population of 845 employees, and a sample of 52 employees to be selected from the population. We can write the names of all employees and put them in a jar and randomly select the 52 employees.

  7. Sampling Methods and the Central Limit Theorem 2- Systematic Random sampling The items or individuals of the population are arranged in some order. A random starting point is selected and then every kth member of the population is selected for the sample.

  8. Sampling Methods and the Central Limit Theorem Example; A population of 2000 sales invoices, a sample of 100 invoices to be selected to estimate the mean dollar revenue. 1- calculate K by dividing the population size by the sample ; (2000/100) = 20th. 2- point a random number, let us say 18, then Every 20th invoice will be selected for the sample. ( 18,38,58,78,98,….).

  9. Sampling Methods and the Central Limit Theorem 3- Stratified random sampling A population is first divided into subgroups, called strata, and a sample is selected from each stratum. For example; College students can be grouped as full time or part time, male or female, then we can apply simple random sampling within each group.

  10. Sampling Methods and the Central Limit Theorem Example; page 216-217

  11. Sampling Methods and the Central Limit Theorem 4- Cluster Sampling A population is first divided into clusters or primary units then samples are selected from the primary units. Suppose you divide a state into 12 primary units , then selected at random four regions ( 2,7,4,12), you could take a random sample of the residents in each of these regions and interview them.

  12. Sampling Methods and the Central Limit Theorem Exercises page 218

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