Download Holt McDougal Algebra 2 8-5

8-5
8-5 Sampling
SamplingDistributions
Distributions
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
Algebra 2Algebra 2
Holt
8-5 Sampling Distributions
Warm Up
Decide whether each sampling
method is likely to result in a biased
sample.
1. The first 30 students to arrive at school are
asked whether they will attend a dance. yes
2. Fifty students are randomly selected from
the roster and asked whether they will attend
a dance.
no
Holt McDougal Algebra 2
8-5 Sampling Distributions
Warm Up : Continued
A café owner wants to know how
many people in the area would come
for Sunday brunch. She asks 20
customers that come for dinner on a
Sunday.
3. Is the sample likely to be representative of
the population?
no
Holt McDougal Algebra 2
8-5 Sampling Distributions
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.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Vocabulary
simple random sample
systematic sample
stratified sample
cluster sample
convenience sample
self-selected sample
probability sample
margin of error
Holt McDougal Algebra 2
8-5 Sampling Distributions
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.
Holt McDougal Algebra 2
8-5 Sampling Distributions
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.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Holt McDougal Algebra 2
8-5 Sampling Distributions
Holt McDougal Algebra 2
8-5 Sampling Distributions
Example 1:Classifying a Sample
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.
This is a systematic sample as members are chosen
using a pattern.
B. They randomly select 100 voters from each county
to Call.
This is a stratified sample as the county is chosen and
then voters are selected at random.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Example 1:Classifying a Sample continued
C. They ask every person who comes to the next
campaign rally to fill out a survey.
This is a convenience sample as the people at the rally
are easily accessible.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Check It Out! Example 1
The editor of a snowboarding magazine wants to
know the readers’ favorite places to snowboard.
The latest issue of the magazine included a
survey, and 238 readers completed and returned
the survey. Classify the sample.
This is a self-selected example as readers
volunteered to participate.
Holt McDougal Algebra 2
8-5 Sampling Distributions
A probability sample is a sample where every
member of the population being sampled has a
nonzero probability of being selected. Simple random
samples, stratified samples, and cluster samples are
all examples of probability sampling.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Example 2: Evaluating Sampling Methods
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
Randomly select
60 people from
the complete
membership list.
Holt McDougal Algebra 2
Method B
Choose every
5th person who
arrives at the
com-munity
clean-up event.
Method C
Randomly select
20 teenagers, 20
adults, and 20
seniors from the
complete roster.
8-5 Sampling Distributions
Example 2:Continued
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.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Check It Out! Example 2
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
Method B
Method C
Ask readers to Survey 10 randomly
Randomly
write in and
selected female
choose 10
give their
students and 10
streets in the
opinion.
randomly selected
town and survey
male students in the
everyone who
cafeteria during the
lives on each
lunch period.
street.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Check It Out! Example 2 continued
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.
Holt McDougal Algebra 2
8-5 Sampling Distributions
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
Holt McDougal Algebra 2
8-5 Sampling Distributions
Example 3: Interpreting a Margin of Error
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.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Check It Out! Example 3
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%.
Holt McDougal Algebra 2
8-5 Sampling Distributions
Lesson Quiz: Part I
The members of a club include 22 freshmen, 61
sophomores, 49 juniors, and 31 seniors. The
club is deciding whether to have a bake sale or
a car wash.
1. Classify each sampling method.
Method A: Survey every 5th
person at Monday’s meeting.
simple random
Method B: Randomly select 40
members to survey.
systematic
Method C: Randomly select and
survey 10 members from each
class.
stratified
Holt McDougal Algebra 2
8-5 Sampling Distributions
Lesson Quiz: Part II
2. Which method from Question 1 is most accurate?
Explain.
Method B is the most accurate because every
member of the population is equally likely to be
in the sample.
3. A survey shows that 55% will vote yes and 45%
will vote no on an issue, with a 7% margin of error.
Explain whether there is a clear preference on the
issue.
No; the intervals defined by the margin of error
overlap from 48–52
Holt McDougal Algebra 2