STAT 218
Week 4
Test / Chapter 6
TEST – Chapters 15
CHAPTER 6 – ESTIMATION AND STATISTICAL INFERENCE
REVIEW STATEMENTS
Recall  comment #1
•
We estimate unknown population parameters by sample statistics
o
E.g: Means for quantitative variables
•
It is an estimate but it is not necessarily accurate
•
How do we know HOW ACCURATE it is?
•
How confident are we that our estimate is close?
•
How close is it?
Recall – comment #2
•
The standard deviation of the mean got smaller as the sample size increased.
•
Actually by square root of n
Consider the survey of the number hours per week you spent listening to music
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Estimate the average based upon a sample of size n = 4
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If we repeated it again, we would not get the same mean. The estimate changes
from sample to sample
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The larger the sample, the more confidence we have to estimate the population
quantity
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This leads to the concept of a confidence interval
Standard Error
•
The standard deviation of the mean is called the Standard Error
•
Sec section 5.3 for previous discussion
•
Standard error
= s / √n
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The difference between the sample mean and the population mean (µ) is rarely
more than a few standard errors
•
Reliability or precision of the estimate of the sample mean as an estimator of the
population mean (µ)
Standard Deviation vs Standard Error
•
SD describes the dispersion of the data
•
SE describes the uncertainty of the mean of the data.
1
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The Standard Error incorporates two factors that affect reliability of the estimate
of the mean
Inherent variability of the data
(s)
The sample size (n)
Draw picture of s vs st.error showing change as n increases
SOME CONVENIENT DEFINITIONS
An
estimat
e is a specific value or quantity obtained for a statistic such as the
mean.
An
unbiased estimator
is one that produces an estimate that is expected to be
equal to the population parameter
A
point estimate
is a single number used to estimate a population parameter.
An
interval estimate
is a spread or interval of values used to estimate a
population parameter
The
confidence coefficient
refers to the probability of correctly including the
population parameter in the interval that is being produced. The probability is
designated as
“1.0 – alpha” The level of confidence is referred to as a percentage
(1.0 – “alpha”) x 100%
Confidence Intervals
are the interval estimates based upon the confidence levels
and are know as
confidence limits
.
ESTIMATION  CONFIDENCE INTERVALS
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 Spring '08
 staff
 Statistics, Normal Distribution, Standard Error, representative

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