Discussion Post: Research Methodology
a) Sampling distribution and central limit theorem. Include hypothetical examples for better clarity.
b) What is a 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 are some of these limitations bypassed?
c) What test statistic is used for constructing a confidence interval on the population's proportion?
d) Why and when is the t statistic used in constructing a confidence interval for the mean of a population?
The response must include a reference list. Using Times New Roman 12 pnt font, double-space, one-inch margins, and APA style of writing and citations.