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COMPLETE BUSINESS STATISTICS

Chapter 5 . Sampling and Sampling Distributions. . Using StatisticsSample Statistics as Estimators of Population ParametersSampling DistributionsEstimators and Their PropertiesDegrees of FreedomThe Template. Sampling and Sampling Distributions. 5. Take random samples from populatio

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COMPLETE BUSINESS STATISTICS

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    1. COMPLETE BUSINESS STATISTICS by AMIR D. ACZEL & JAYAVEL SOUNDERPANDIAN 6th edition (SIE)

    2. Chapter 5 Sampling and Sampling Distributions

    3. Using Statistics Sample Statistics as Estimators of Population Parameters Sampling Distributions Estimators and Their Properties Degrees of Freedom The Template

    4. Take random samples from populations Distinguish between population parameters and sample statistics Apply the central limit theorem Derive sampling distributions of sample means and proportions Explain why sample statistics are good estimators of population parameters Judge one estimator as better than another based on desirable properties of estimators Apply the concept of degrees of freedom Identify special sampling methods Compute sampling distributions and related results using templates

    5. 5-1 Using Statistics

    6. The Literary Digest Poll (1936)

    7. An estimator of a population parameter is a sample statistic used to estimate or predict the population parameter. An estimate of a parameter is a particular numerical value of a sample statistic obtained through sampling. A point estimate is a single value used as an estimate of a population parameter. 5-2 Sample Statistics as Estimators of Population Parameters A sample statistic is a numerical measure of a summary characteristic of a sample.

    8. Estimators

    9. The population proportion is equal to the number of elements in the population belonging to the category of interest, divided by the total number of elements in the population: Population and Sample Proportions

    10. A Population Distribution, a Sample from a Population, and the Population and Sample Means

    11. Stratified sampling: in stratified sampling, the population is partitioned into two or more subpopulation called strata, and from each stratum a desired sample size is selected at random. Cluster sampling: in cluster sampling, a random sample of the strata is selected and then samples from these selected strata are obtained. Systemic sampling: in systemic sampling, we start at a random point in the sampling frame, and from this point selected every kth, say, value in the frame to formulate the sample. Other Sampling Methods

    12. The sampling distribution of a statistic is the probability distribution of all possible values the statistic may assume, when computed from random samples of the same size, drawn from a specified population. The sampling distribution of X is the probability distribution of all possible values the random variable may assume when a sample of size n is taken from a specified population. 5-3 Sampling Distributions

    13. Sampling Distributions (Continued)

    14. There are 8*8 = 64 different but equally-likely samples of size 2 that can be drawn (with replacement) from a uniform population of the integers from 1 to 8: Sampling Distributions (Continued)

    15. Sampling Distributions (Continued)

    16. Comparing the population distribution and the sampling distribution of the mean: The sampling distribution is more bell-shaped and symmetric. Both have the same center. The sampling distribution of the mean is more compact, with a smaller variance. Properties of the Sampling Distribution of the Sample Mean

    17. Relationships between Population Parameters and the Sampling Distribution of the Sample Mean

    18. Sampling from a Normal Population

    19. The Central Limit Theorem

    20. The Central Limit Theorem Applies to Sampling Distributions from Any Population

    21. The Central Limit Theorem (Example 5-1)

    22. Example 5-2

    23. The t is a family of bell-shaped and symmetric distributions, one for each number of degree of freedom. The expected value of t is 0. The variance of t is greater than 1, but approaches 1 as the number of degrees of freedom increases. The t is flatter and has fatter tails than does the standard normal. The t distribution approaches a standard normal as the number of degrees of freedom increases. Students t Distribution

    24. The Sampling Distribution of the Sample Proportion,

    25. Sample Proportion (Example 5-3)

    26. Desirable properties of estimators include: Unbiasedness Efficiency Consistency Sufficiency 5-4 Estimators and Their Properties

    27. Unbiasedness

    28. Unbiased and Biased Estimators

    29. Efficiency

    30. Consistency and Sufficiency

    31. Properties of the Sample Mean

    32. Properties of the Sample Variance

    33. 5-5 Degrees of Freedom

    34. Degrees of Freedom (Continued)

    35. Degrees of Freedom (Continued)

    36. Example 5-4

    37. Example 5-4 (continued)

    38. Example 5-4 (continued)

    39. Using the Template

    40. Using the Template

    41. Using the Template

    42. Using the Template

    43. Using the Computer

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