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CHAPTER 10:
INTRODUCTION TO ESTIMATION
Stats & Prob. for Bus. Mgmt (Stat1100)
Jochem
Chap 10: Intro to Estimation
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Overview/Goals
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1. Understand the 2 Types of Estimators
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2. Be able to estimate the Population Mean when the
Population Standard Deviation is known
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3. Be able to Determine the appropriate Sample Size
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Chap 10: Intro to Estimation
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0. Where we left off
Population &
Parameters
Individual Member
of Population
Probability distribution
Chap 68
Population &
Parameters
Sample Statistics
Sampling distribution
Population &
Parameters
Sample Statistics
Sampling distribution
Chap 9
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Chap 10: Intro to Estimation
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1. Types of Estimators
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Point Estimator
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Estimates the value of an unknown parameter through a
single value/point.
Problems:
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1. it is unlikely (in fact, the probability is 0) that an estimator that
is based on a sample that is smaller than the population has the
exact same value as a continuous statistic.
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2. We have no information about how close the estimator is to
the true parameter.
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3. Point estimators do not reflect the greater accuracy that
originates from an increasing sample size.
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Chap 10: Intro to Estimation
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1. Types of Estimators
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Interval Estimator
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Using an
interval
as an estimation to an unknown parameter
(e.g., “
μ
lies in between 50.3 and 50.7”).
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Chap 10: Intro to Estimation
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1. Concepts of Estimation
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3 desirable Characteristics for an Estimator
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1. Unbiasedness
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If we repeatedly drew samples from the population, then for each
sample it is equally likely that the estimate is above or below the
true parameter.
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expected value of an unbiased estimator
across many samples is equal to the true parameter.
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Chap 10: Intro to Estimation
box2
1. Concepts of Estimation
box5
3 desirable Characteristics for an Estimator
square6
1. Unbiasedness
square6
If we repeatedly drew samples from the population, then for each
sample it is equally likely that the estimate is above or below the
true parameter.
barb2right
expected value of an unbiased estimator
across many samples is equal to the true parameter.
square6
2. Consistency
square6
the difference between the estimator and the parameter grows
smaller as the sample size increases.
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Chap 10: Intro to Estimation
box2
1. Concepts of Estimation
box5
3 desirable Characteristics for an Estimator
square6
1. Unbiasedness
square6
If we repeatedly drew samples from the population, then for each
sample it is equally likely that the estimate is above or below the
true parameter.
barb2right
expected value of an unbiased estimator
across many samples is equal to the true parameter.
square6
2. Consistency
square6
the difference between the estimator and the parameter grows
smaller as the sample size increases.
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 Spring '08
 Chiappetta
 Normal Distribution, Standard Deviation, UCL, LCL

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