This This question is based on Intro to mathematical statist

This This question is based on Intro to mathematical statistics

Solution

Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state — the collection and analysis of facts about a country: its economy, land, military, population, and so forth.

Statistical science is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling. The initial analysis of the data from properly randomized studies often follows the study protocol.

Of course, the data from a randomized study can be analyzed to consider secondary hypotheses or to suggest new ideas. A secondary analysis of the data from a planned study uses tools from data analysis.

Data analysis is divided into:

While the tools of data analysis work best on data from randomized studies, they are also applied to other kinds of data --- for example, from natural experiments andobservational studies, in which case the inference is dependent on the model chosen by the statistician, and so subjective.^[3]

Mathematical statistics has been inspired by and has extended many options in applied statistics.