Download Chapter 21 Notes

Confidence Intervals
(Dr. Monticino)
Assignment Sheet
Read Chapter 21
Assignment # 14 (Due Monday May 2nd )
 Chapter 21
• Exercise Set A:
• Exercise Set B:
• Exercise Set C:
• Exercise Set E:
1,2,3,7
1-4
1-8
1,2,3
 Review Exercises: Try them all … not to turn in.
(good review for Final Exam)
Overview
Confidence intervals for survey
sampling
Knowing/Not Knowing the
Percentages
Up to now, have assumed that know
composition of population being sampled
 Example: Know the percentage of population of a
particular type
• Have calculated the probability that a randomly drawn
sample will have a certain sample percentage
Now will draw a sample without knowing
composition of population
 Want to infer value of population parameter from
sample statistic AND want to measure how
reliable is the sample statistic
Confidence Intervals
A confidence interval for a parameter
estimate provides a measure of the accuracy
of the estimate
A c% confidence interval is a random
interval, calculated from the sample, which
has a c% probability of containing the
population parameter
 Example: 95% percent of the time a 95%
confidence interval will contain the population
parameter
Components of a Confidence Interval
Calculation
Parameter statistic
 A parameter statistic is the population parameter
estimate obtained from the sample
• Sample mean
• Sample percentage
Population variance
 The sample is used to estimate how much the
population values vary
• Population standard deviation is estimated with sample
standard deviation (for large samples)
• Use corrected sample standard deviation (for small
samples)
Components of a Confidence Interval
Calculation
Standard error
 The standard error of the sample measures the
likely amount that the sample statistic is off from
the population parameter
 Often use
SE 
SD
Sample size
Confidence Level
 The confidence level indicates how confident you
should be that population parameter lies in the
confidence interval
• Use the normal approximation given by the Central
Limit Theorem
Confidence Intervals
General form of a confidence interval is
(sample statistic) +/- (standard units associated
with c% confidence interval)*(SE)
 sample

 statistic
 sample

 statistic
  standard units associated
  
  with c% confidence interval
  standard units associated
  
  with c% confidence interval

 sample
  SE, 

 statistic

  SE

  standard units associated
  
  with c% confidence interval


  SE 


Example
A survey was conducted to determine
the proportion of current UNT students
who would be interested in enrolling in
a web-based statistics course. In the
survey of 500 students, 200 of the
students expressed interest. Determine
the 95% confidence interval for the
percentage of students interested in a
web-based course.
Example
Suppose now that all UNT students were
surveyed and the proportion of students
who were interested in a web-based math
course was .28. If appropriate, calculate
the 95% confidence interval.
Cautions and Notes
The standard deviation of the sample can be
used as an estimate for the standard deviation
of the population if
 the sample is large enough
• “Large enough” depends on many factors
 the sample is obtained by simple random
sampling
Cautions and Notes
The standard deviation says how far an
element in the population differs from the
population average, for a typical element
The standard error says how far the sample
average differs from the population average,
for a typical sample
Most methods for calculating confidence
intervals assume simple random sample
 These methods are not appropriate for other types
of samples
Cautions and Notes
If the sample is selected from the population
without replacement and the sample is large
with respect to the population, then a
correction factor is needed for the standard
error
SE without replacement =
population  sample
population  1
 SE with replacement
Cautions and Notes
Confidence intervals for small samples are
tricky to calculate. When in doubt
 Select a larger sample
 Consult a statistician
If the sample data show a trend or pattern
over time, then the above techniques do not
apply to estimating parameter values or
determining their accuracy
(Dr. Monticino)