Lecture 12 - Lecture 12 Material Covered in This Lecture...

Lecture 12
Material Covered in This Lecture:
1
C Chapter 6, Section 6.1: Estimating with Confidence
1 1. Introduction
There are two types of statistical inferences:
(1) Confidence interval;
(2) Tests of significance.
Both types of inference are based on the sampling distributions of
statistics.
2. Confidence Interval
(1). The reasoning of constructing the confidence interval.
Example: Suppose the entire population of SAT scores has mean μ
and standard deviation σ. We want to estimate the population mean μ
based on the sample X
1
, X
2
, …, X
500
.
When the sample size n is large (in this example, n=500), the sample
mean
X
is a good estimator (Law of large number). Sample mean
X
is
a point estimation of the population mean μ.
X
cannot capture the variation among the samples. Confidence
interval can do this work!
It can tell us how likely an interval can cover the true population
mean if the same estimation procedure repeated many times.