Chapter 2

1. obtain sample from the population
2. measure the sample.
3. make conclusions about the population.

Two Reasoning Processes:

• Deductive reasoning: general -> particular
• Inductive reasoning: particular -> general

goal of statistical inference

learn something about the population by studying a random sample. Consider a property of the population $X$, measured by a single number $\mathrm{\Theta }$ goal is to estimate the value of Theta with some function $T(x_1,...x_n)$

Statistic

A function $T(x_1,...x_n)$ of a random sample $\{x_1,...,x_2\}$ is called a statistic. The statistic $T(x_1,...,x_n)$ is an estimate for $\mathrm{\Theta }$

Notation

$T(x_1, ..., x_n) = $