Topic 16 Interval Estimation - University of Arizona
Overview
Means
Correspondence between Two-Sided Tests and Confidence Intervals
Interpretation of the Confidence Interval
Topic 16 Interval Estimation
Confidence Intervals for Means
1 / 21
Overview
Means
Correspondence between Two-Sided Tests and Confidence Intervals
Interpretation of the Confidence Interval
Outline
Overview
Means z intervals t intervals
Correspondence between Two-Sided Tests and Confidence Intervals Two Sample t intervals
Interpretation of the Confidence Interval
2 / 21
Overview
Means
Correspondence between Two-Sided Tests and Confidence Intervals
Overview
Interpretation of the Confidence Interval
The quality of an estimator can be evaluated using its bias and variance. Often, knowledge of the distribution of the estimator and this allows us to take a more comprehensive statement about the estimation procedure.
For interval estimation, given data x, we replace the point estimate ^(x) for the parameter , the parameter space by a statistic that is subset C^(x) . We consider both the classical and Bayesian approaches.
3 / 21
Overview
Means
Correspondence between Two-Sided Tests and Confidence Intervals
Interpretation of the Confidence Interval
Overview
For a given parameter value , the coverage probability of C^(X ) is
P{ C^(X )}, The C^(X ) is typically chosen to have a prescribed high probability, , of containing the true parameter value .
P{ C^(X )} for all , C^(x) is called a -level confidence set. For a single parameter, the typical choice of confidence set is a confidence interval. This can be two-sided.
C^(x) = {; ^ (x), ^u(x)} = [^ (x), ^u(x)].
4 / 21
Overview
Means
Correspondence between Two-Sided Tests and Confidence Intervals
Interpretation of the Confidence Interval
Overview
Often this interval takes the form [^(x) - m(x), ^(x) + m(x)] = ^(x) ? m(x) where the two statistics,
? ^(x) is a point estimate, and m(x) is the margin of error.
For one-sided confidence intervals, we can have
C^(x) = {; ^u(x)} = (-, ^u(x)]. where ^u(x) is called the upper confidence bound or
C^(x) = {; ^u(x) } = [^ (x), ). where ^ (x) is called the lower confidence bound
5 / 21
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- package intervals
- you are now the proud owner of a seiko radio wave controlled worldtimer
- using your ti nspire calculator estimating a population proportion 1
- topic 16 interval estimation university of arizona
- mr c miller home
- 6 1 graphs of normal probability distributions
- chapter 6 confidence intervals and hypothesis testing using z for the
- interval notation union and intersection calculator
- worksheet 5 2 normal distributions finding probabilities
- confidence intervals z scores university of alberta
Related searches
- university of arizona salaries
- university of arizona salary list
- university of arizona salary 2018
- university of arizona financial
- university of arizona address tucson
- university of arizona admissions status
- university of arizona application 2020
- university of arizona arthritis center
- university of arizona rheumatology
- university of arizona body donation
- university of arizona employment
- university of arizona salary grades