Download Introduction to Decision Analysis

Chance Errors in
Sampling
(Dr. Monticino)
Assignment Sheet
Read Chapter 20
Assignment # 13 (Due Wed. April 27th )
Chapter 20
• Exercise set A: 2,3,4;
• Exercise set B: 1,2,3
• Exercise set C: 2,3,4
Overview
Review Central Limit Theorem for
averages (percentages)
Examples
Correction factor when sampling
without replacement
Central Limit Theorem:
Averages
For a large number of random draws, with
replacement, the distribution of the average =
(sum)/N approximately follows the normal
distribution
 The mean for this normal distribution is
• (expected value for one repetition)
 The SD for the average (SE) is

N
This holds even if the underlying population
is not normally distributed
Examples
 Suppose that 25% of likely voters are undecided on who
they will vote for in the upcoming presidential election. 400
eligible voters are selected at random
 What is the expected number of people in the sample that will be
undecided?
 What is the expected percentage of people in the sample that will be
undecided?
 What is the SE for the number of people in the sample that will be
undecided?
 What is the SE for the percentage of people in the sample that will be
undecided?
 What is the probability that between 70 and 90 people in the sample
will be undecided
 What is the probability that between 18% and 22% of the people in
the sample will be undecided
 Between what two values (centered on the expected percentage) will
95% (99%) of the sample percentages lie?
Accuracy of Percentages
The accuracy of the sample percentage
is determined by the absolute size of the
sample, not the size relative to the
population
Example…
Correction Factor
 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
 “When the number of tickets in the box (population)
is large relative to the number of draws (sample), the
correction factor is nearly 1 and can be ignored.”
(Dr. Monticino)