### Tedext ### Statistics for Business, Economics - Sampling Distributions

WK3-Discussion Question 1 (CLO’s 1, 2, 3)

•           •Readings: Anderson et al, Statistics for Business and Economics

o Chapter 7: Sampling and Sampling Distributions

o Chapter 8: Interval Estimation

Book link:

Statistics for Business and Economics 13th 13E.pdf

•           •Please define each of the following terms: sampled population, random sampling, convenient sampling, judgmental sampling, stratified random sampling, consistency in sampling, relative efficiency. Explain why a sample is of probabilistic nature.

•           •What is it meant by the term “parameter of a population”? Explain why a population can be represented by a random variable.

•           •What is a point estimate, and an unbiased point estimate? Explain how the sample mean can be an unbiased estimate of the population mean. How do you justify that the sample variance is an unbiased estimate of the population variance? What is the sampling requirement in the latter case? Provide a numerical example of estimating the mean, the variance, and the standard deviation.

•           •Please define each of the following terms, discuss applicability and significance of each: sample statistic, standard error, sampling distribution, and central limit theorem. Include hypothetical examples for better clarity.

•           •What is the z statistic and what qualifies a statistic to be z statistic based on the central limit theorem and the basic properties of normal distributions? What are the limitations of the central limit theorem, and how some of these limitations are bypassed? For example, the z statistic as the sampling distribution in estimating a proportion.

•                                                  •What is the sampling distribution in estimating the variance of a population? What are the properties of this distribution?

•           •What is the alternative of z statistic for normally distributed populations which eliminates some limitations of the central limit theorem? How this sampling distribution is constructed as combination of a z distribution and a chi squared distribution? What are the properties of this distribution?

(To provide numerical examples to answer questions mentioned above, for example, in the third item above, you can use the Excel function RAND to generate a sample of a uniform random variable, and the combination of RAND and NORM.INV to generate a sample of a normal random variable). Please be sure to include in-text citations and peer reviewed references in your discussion post.

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