1
Chapter 9:
Point Estimates and Confidence Intervals
1.
Review of Sampling
a.
Sample is a subset of a population
b.
Reasons for sampling
i.
To contact the whole population would be very time consuming
ii.
The cost of studying all the items in the population is prohibitive
iii.
It is physically impossible to check all the items in the population
iv.
The nature of the test is destructive
v.
A sample adequately represents the rest of the population
c.
Methods of sampling
i.
Simple random sampling
ii.
Systematic random sampling
iii.
Stratified random sampling
iv.
Cluster sampling
b.
Sampling error is the difference between a sample statistic and its
corresponding population parameter
i.
Example:
X
μ
!
c.
Sampling distribution
i.
Suppose all
possible samples of size n are selected from a specified
population, and the mean of each sample is computed. We could
then find the distribution of all the means.
ii.
The mean of all the sample means is exactly equal to the
population mean
iii.
If the population from which the samples are drawn is normal, the
distribution of the sample means is also normally distributed
iv.
If the population from which the samples are drawn is not normal,
the sampling distribution is approximately normal if the samples
are sufficiently large (at least 30 observations or if binomial data
then
5
n
!
>
and
(1
)
5
n
"
>
)
2.
Statistical Inferences
a.
We use sampling to estimate characteristics of the population
i.
Parameter is a characteristic of the population
ii.
The population is large or it is difficult to identify all members of
the population and so we are unable to take all possible samples
from the population.
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b.
Point estimate
i.
A point estimate is a single statistic used to estimate a population
parameter
ii.
Example of point estimates
1.
The sample mean,
X
, is a point estimate for the population
mean,
μ
2.
The sample proportion, p, is a point estimate for the
population proportion,
!
3.
The sample standard deviation, s, is a point estimate for the
population standard deviation,
Parameter
Statistic
Mean
x
Standard deviation
s
Proportion
p
Correlation
r
iii.
We expect the point estimate to be close to the population
parameter but not exactly the same as the population parameter due
to sampling error
iv.
Example: A manufacturer of batteries for portable hand tools
wishes to investigate the length of time a battery will last. A
sample of 12 batteries had a mean length of time of 4.3 hours. We
know that the standard deviation of battery life is 0.3 hours for the
population.
1.
Why do we sample in this case?
2.
What is the point estimate?
3.
If all the batteries last an average of 4 hours, what is the
sampling error?
c.
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 Spring '08
 Dr.Lohaka
 Normal Distribution, Standard Deviation, Ohio Unemployment Commission, Jiffy Supermarket

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