A Sample of 4 Clusters Is to Be Taken from a Population

question 62

Essay

A sample of 4 clusters is to be taken from a population with N = 50 clusters and M = 800 elements in the population. The values of M_i and X_i for each cluster are shown below.
a.Determine the point estimate of the population mean.
b.Determine the standard error of the mean.
c.Develop a 95% confidence interval for the population mean.
d.Determine the point estimator of the population total.
e.Approximate a 95% confidence interval estimate of the population total.

---

Definitions:

Substantive Rationality

Substantive rationality refers to decision-making and reasoning based on the consideration of ends, values, or goals, rather than solely on predetermined rules or procedures.

Lifeworld

A term in philosophy and social sciences referring to the individual's personal world of experience and meaning separate from systemic structures.

Micro Social Phenomena

refers to the small-scale social events and interactions between individuals or small groups that contribute to the larger societal structure.

Macro Social Phenomena

Large-scale social processes and structures that influence societies and individuals, such as institutions, trends, and demographic changes.