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26134 Business Statistics
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Tutorial 10: Confidence Intervals
Introduction: Key concepts in this tutorial are listed below
Confidence Interval: Point estimate ± critical value * standard error
Sample Statistic ± critical value * standard error
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In statistics we usually want to statistically analyse a population but collecting data
for the whole population is usually impractical, expensive and unavailable. That is
why we collect samples from the population (sampling) and make inferences about
the population parameters using the statistics of the sample (inferencing) with some
level of accuracy (confidence level).
Statistical inference is the process of
drawing conclusions about the entire
population based on information in a
sample by:
• constructing confidence intervals on
population parameters
• or by setting up a hypothesis test on a
population parameter
Sample Size N
n
A population is a collection of all possible individuals, objects, or measurements of
interest. A sample is a subset of the population of interest.
Motivation-Point estimator
The objective of estimation is to determine the value of a
population parameter on the basis of a sample statistic.
EXAMPLE: “What is the average time taken by
Parameter ()
customers on a single shopping trip?
We can use sample data to
calculate the sample mean
(xbar). Using this single
value, we can infer about
population parameter
(mu).The sample mean, a
single value, is referred to
as the point estimate.
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Population distribution
(of X)
Sample distribution
(of 𝑋)
@ Dr. Sonika Singh, BSTATS, UTS
Point estimate (e.g., 𝑋)
Motivation-Interval estimator
To make statements about unknown population parameter with
greater accuracy/confidence, we can develop an interval
estimator.
Parameter
Population distribution
Sampling distribution
Interval estimate
An interval estimate draws inferences about a population
by estimating the value of an unknown population
parameter using an interval. This interval is called as the
Confidence Interval (CI).
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@ Dr. Sonika Singh, BSTATS, UTS
Confidence Intervals
Interval Estimates - Interpretation
• Confidence Interval: a range of values
constructed from sample data so that
the population parameter is likely to
occur within that range at a specified
probability. The specified probability is
called the level of confidence.
• Common levels of confidence used
by analysts are 90%, 95%, and 99%.
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• A 95% confidence interval
indicates that approximately 95 of
the 100 confidence intervals
would contain the population
mean.
@ Dr. Sonika Singh, BSTATS, UTS
Confidence Intervals
Confidence Intervals
Confidence Intervals
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