Transcript 2.2 Sabrina notes random sampling and MOE

Objectives
Estimate population means and proportions
and develop margin of error from simulations
involving random sampling.
Analyze surveys, experiments, and
observational studies to judge the validity of
the conclusion.
Vocabulary
simple random
sample
systematic
sample
stratified sample
cluster sample
convenience
sample
self-selected
sample
probability
sample
margin of error
Which are
random
Sampling
methods?
Which are
nonrandom
Sampling
methods?
When a survey is used to gather data, it is
important to consider how the sample is selected
for the survey. If the sampling method is biased,
the survey will not accurately reflect the
population.
Most national polls that are reported in the news
are conducted using careful sampling methods
in order to minimize bias.
Other polls, such as those where people phone
in to express their opinion, are not usually
reliable as a reflection of the general population
Remember that a random sample is one that
involves chance. Six different types of samples
are shown below.
The campaign staff for a state politician wants to know how voters in the state feel about a
number of issues. Classify each sample.
A. They call every 50th person on a list of registered voters in the state.
B. They randomly select 100 voters from each county to call.
Use the Venn Diagram to
compare and contrast
systematic vs. stratified
sampling
Systematic
Stratified
C. They ask every person who comes to the next campaign rally to fill out a survey.
D. The local news asks its viewers to call-in or text their opinions.
Self-selected
Use the Venn Diagram to
compare and contrast
self-selected vs. convenience
sampling
Convenience
E. They randomly select 100 voters from each county to call.
F. They randomly select 5 counties from the region and contact every voter within each of
those counties.
Stratified
Use the Venn Diagram to
compare and contrast
stratified vs. cluster
sampling
Cluster
A community organization has 56 teenage members, 103 adult members, and 31 senior members. The
council wants to survey the members. Classify each sampling method. Which is most accurate? Which is
least accurate? Explain your reasoning.
Method A: simple random
Method B: systematic
Method C: Stratified
Method A is the most accurate because every member of the population
is equally likely to be in the sample. In Method C, the sample contains an
equal number from each group, but the total numbers in each group differ
significantly. So, adults are underrepresented and seniors are
overrepresented. Method B is the least accurate because members who
do not attend the cleanup have no chance of being included.
A small-town newspaper wants to report on public opinion about the new City Hall
building. Classify each sampling method. Which is most accurate? Which is least
accurate? Explain your reasoning.
Method A: self-selected
sample
Method B: convenience
sample
Method C: cluster sample
Method A is the least accurate because only people who are
willing to volunteer their opinions are chosen. Method B is also
inaccurate because only students and only those in the
cafeteria are surveyed. Method C is the most accurate
because different groups are randomly chosen and then all
members of the chosen group are surveyed.
Application: Two classes each had 10 qualified students volunteer for
junior cabinet. Only 4 students total can be selected. Ms. Mashburn
decides that she must randomly select the 4 to serve.
Class A:
Class B:
Allison
Jason
Annie
John
Belinda
Keith
Barbara
Ken
Calissa
Lon
Corinne
Lewis
Jennifer
Mark
Judy
Mike
Margaret
Ned
Madison
Norm
Explain how could you help Ms. Mashburn choose the 4 students
randomly. Implement each sampling strategy by using the table of
random digits below. Write down who was chosen.
SRS...Simple Random Sample
Step 1: Give each student a unique two digit number. Since there are 20 students, you can number them
from 00-19.
start here....
Step 2: Decide where to start in the table
of random digits. Look at two digits at a
time. If it you find a number between
00 and19, find the associated student and
select him/her for your sample. Continue
this process until you find 4 unique students.
Sample chosen: _______________, ______________
___________________, ____________________
Systematic Sample
Step 1: Give each student a unique two digit
number.
Step 2: Use the table of random digits to randomly
pick the first student in your sample. Then choose
start
every 20/4 = 5th student from the one randomly
chosen.
here....
Sample: _________, ___________
____________, _____________
Step 1: Give each student a
two digit number.
Stratified Random Sample...by gender
Step 2: Use your table of digits to
pick until you get two unique girls
and 2 unique boys. Ignore repeated
values. Also, if you select two girls first,
then ignore all other girls and continue
until you get two boys.
start here....
Sample: ____________, ______________
______________, ________________
Step 1: Give each cluster a
number. Since there are 5 groups, you
can assign them the numbers from
00-04.
Cluster Sample
Step 2: Use the table until you find
a number between 00-04. Everyone
in that group will be in your sample.
start here....
Sample: ____________, ______________
______________, ________________
The margin of error of a random sample
defines an interval, centered on the sample
percent, in which the population percent is most
likely to lie
A city is about to hold an election. According to a survey
of a random sample of city voters, 42% of the voters plan
to vote for Poe and 58% of the voters plan to vote for
Nagel. The survey’s margin of error is ±7%. Does the
survey clearly project the outcome of the voting?
Between 35% and 49% of all voters plan to vote for Poe and
between 51% and 65% of all voters plan to vote for Nagel.
Because the intervals do not overlap, the survey does clearly
project the outcome of the voting.
A survey of a random sample of voters shows that
38% of voters plan to vote for Gonzalez, 31% of
voters plan to vote for Chang, and 31% plan to vote
for Harris. The survey has a margin of error of
±3%. Does the survey clearly project the outcome
of the voting? Explain.
Yes; while there is overlap between the intervals for
Chang and Harris, their intervals, which are from 28%
to 34%, do not overlap the interval for Gonzalez, which
is 35% to 41%.