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SP 225
Lecture 11
Confidence Intervals
Three Separate Distributions
 Sample distribution


Empirical and known
Intended to help learn about the population
 Population distribution


Empirical and unknown
Properties estimated using statistics
 Sampling distribution


Theoretical or non-empirical
Properties well-known and based on probabilities
Example Problem
A researcher has gathered information from a
population with an average of 2.3 people and a
standard deviation of 0.35. If the researcher
collects samples of 100 households, what
proportion of samples will have a mean less
that 2.25?
Confidence Interval
 Mathematical statement that says that
the parameter lies within a certain range
of values
 95% confident that the mean length of
employment at XYZ automotive is
between 8 and 12 years
Probability Distribution for
Population Mean
 95% confident that the mean length of
employment at XYZ automotive is
between 8 and 12 years
(sample)
Confidence Interval Example
 A random sample of 100 television
programs contained an average of 2.37
acts of physical violence per program.
The standard deviation of the number of
acts of violence on television in the
population is 3. At the 99% level, what is
your estimate of the mean number of
acts of violence for all television
programs?
Confidence Interval Formula
c.i.  X  Z (

N
)
Confidence Interval Estimate
s
c.i.  X  Z (
)
N 1
Confidence Interval Example 2
 A researcher has gathered information
from a random sample of 178
households. The households averaged
6.0 hours of television viewing per day
with a standard deviation in the sample
of 3.0 hours. Construct a 90%
confidence interval for the hours of
television watched per day in the
population.
Alpha
 Percent of confidence intervals that DO
NOT contain the population mean over
the long run
 Probability this confidence interval
DOES NOT contain the population mean
 Width of confidence interval
 Complement of confidence level
Efficiency
 Extent to which the confidence interval
clusters around the mean
 Width of the confidence interval
 Determined by population standard
deviation and sample size
Confidence Intervals in SPSS
 Give a 95% confidence interval for the
number of children in an American family
using GSS data.
In-Class
 7.7 a & b