Confidence interval estimation

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STAM4000
Quantitative Methods
Week 7
Confidence interval estimation
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Confidence will be illustrated or
expressed as a percentage of confidence –
this is also called the “confidence level” or
the “confidence percentage”.
Interval is a “range” of values, where will
have a “lower bound” and an “upper
bound”, usually,
(lower bound, upper bound)
estimation refers to two types of
estimation in the Week 7 class; these are
of population parameters:
i. Estimate the population mean
ii. Estimate the population proportion
Confidence Intervals are usually
abbreviated as CI
Today’s topic will be assessed in QQ3:
QQ3:
Week 5: sampling distributions
Week 7: confidence interval
estimation.
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#1
#2
#3
Distinguish between point and interval
estimators
Interval estimation of the population
mean,
μ
Interval estimation of the population
proportion,
p
Week 7
Confidence
interval estimat
Learning
Outcomes

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Why does this matter?
This Photo by Unknown Author is licensed under CC BY-SA-NC
In the real
world, we are
concerned
about the
confidence of
our estimates.
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#1 Distinguish between point and interval estimators
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#1

•A statistic, measured at one point in
time, to estimate a parameter.

Point estimator

A range of values, based on a statisti
to estimate a parameter.

Interval
estimator
Point and interval estimators
Distinguish between point and interval estimation
We have learned about population parameters and sample statistics.
Population parameters are measurements based on an entire population of data.
Sample statistics are measurements based on a sample of data.
Due to the constraints of time, money etc., it is very rare that we have a population of data. We usually base our
statistical analysis on a sample of data. The objective of estimation is to use the value of a sample statistic to give an
approximate value for the corresponding unknown population parameter.
There are two types of estimators:
i. point estimator
ii. interval estimator
A point estimator, of an unknown population parameter, is a single value of the sample statistic, based on one sample,
taken at one point in time.
There are some issues with the point estimator:
Each time we take a sample, we have a different set of values, and hence a different sample statistic as a point
estimator. How do we know which sample was more likely to be representative of the population, and hence which
statistic is the closest approximation to the parameter? We do not know this, and we have no way to quantify this
with a point estimator.
The point estimator ignores the probability distribution, of the statistic, when estimating the parameter.
An interval estimator draws inference about a population parameter. How?
The interval estimator has the following qualities:
Is a range of values
Has the sample statistic as the midpoint of the interval
Uses a measure of dispersion, incorporating the sample size
Uses the concept of “confidence” to offer a degree of precision for the accuracy of the interval estimate. This
“confidence” is quantified as a percentage based on areas under the curve of a statistical distribution e.g. , under the
Z curve.
An interval estimator is called a Confidence Interval (CI).
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Two types of
point estimators
this week
Sample mean,