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Using your textbook, LIRN-based research, and the Internet, apply the learning outcomes for the week/course and lecture, discuss the following concepts and provide numerical/practical examples

● 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 the z statistic for normally distributed populations which eliminates some limitations of the central limit theorem? How is this sampling distribution constructed as a 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). 

Make sure to include in-text citations and peer reviewed references in APA format in your discussion post.