复习统计（1）

parameter 参数 来自母体 例如母体均值μ, 母体标准差 σ

statistic 统计量 来自抽样 例如样本均值x⎯⎯, 样本标准差 s

The objective of statistics is to make inference about a population based on information contained in a sample.

central limit Theorem 中央极限定理

- n≥30, 不论母体之分布,

x¯∼N(μx¯=μ,σx¯=σn√)

- n<30, 母体为正态分布,

x¯∼N(μ,σn√)

- n≥30, 不论母体之分布,

p̂ ∼N(μp̂ =P,σp̂ =P(1−P)n)‾‾‾‾‾‾‾‾‾‾√

Two types of estimation are point estimation and interval estimation.

（1）Point Estimator (点估计): A point estimator of a population parameter is a rule (or formula) that tells you how to calculate a single number based on sample data. The resulting number is called a point estimate of the parameter.

μ:x⎯⎯ σ:s P:p̂

Unbiased estimator (不偏估计量): An estimator of a population parameter is said to be unbiased if the mean of its sampling distribution is equal to the parameter.

E(sample estimator)=population parameter

X⎯⎯⎯, S, and P̂ are unbiased estimator

（2）Interval Estimation (区间估计): an interval estimator of a

population parameter is a rule that tells you how to calculate two numbers based on sample data

Confidence coefficient (信赖系数): the probability that a confidence interval will enclose the estimated parameter is called the confidence coefficient.

信赖系数是小数值；信赖水准是百分值。