7-3 Populations and Samples
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
7-3 Populations and Samples
Warm Up
Solve.
1. 12 2 = n
5 9
n = 1113
5
2. 8n = –0.5
n = –0.0625
3. n – 9 = –14
n = –15
4. –16 = n – (–30)
n = –46
7-3 Populations and Samples
Problem of the Day
Why are both products the same?
26  51 = 1,326
39  34 = 1,326
26  51 = (2  13)  (3  17);
39  34 = (3  13)  (2  17);
They have the same factors: 2, 3,
13, and 17
7-3 Populations and Samples
I can compare and analyze sampling
methods.
7-3 Populations and Samples
Vocabulary
population
sample
random sample
convenience sample
biased sample
7-3 Populations and Samples
In 2002, there were claims that Chronic Wasting
Disease (CWD), or Mad Elk Disease, was
spreading westward across North America. In
order to verify claims such as these, the elk
population had to be tested.
When information is gathered about a group,
such as the elk in North America, the entire
group is called the population. Because testing
each member of a large group can be difficult or
impossible, researchers often study a part of the
population, called a sample.
7-3 Populations and Samples
For a random sample, members of the
population are chosen at random. This gives
every member of the population an equal
chance of being chosen. A convenience
sample is based on members of the population
that are readily available, such as 30 elk in a
wildlife preservation area.
Helpful Hint
A random sample is more likely to
be representative of a population
than a convenience sample is.
7-3 Populations and Samples
Additional Example 1: Analyzing Sampling Methods
Determine which sampling method will better
represent the entire population. Justify your
answer.
Sampling method
Maria surveys only the band students
she knows personally.
Jon writes each band student’s name
on a card. He questions those
students whose name he draws.
Results
84% want
blue uniforms
61% want
blue uniforms
Jon’s sample is a random sample, giving every
band member equal chance to be surveyed, so it
is the better method.
7-3 Populations and Samples
Check It Out: Example 1
Determine which sampling method will better
represent the entire population. Justify your
answer.
Sampling method
Ferdinand surveys every other
swimmer on the team.
Anna-Maria questions the swimmers
who are in her Biology class.
Results
72% want
practice early
50% want
practice early
Ferdinand’s sample is a random sample, giving
results that better represent the entire
swimming team, so it is the better method.
7-3 Populations and Samples
A biased sample does not fairly represent the
population. A study of 50 elk belonging to a
breeder could be biased because the breeder’s
elk might be less likely to have Mad Elk
Disease than elk in the wild.
7-3 Populations and Samples
Additional Example 2: Identifying Potentially
Biased Samples
Determine whether each sample may be biased.
Explain.
A. The mayor surveys 100 supporters at a rally
about the most important issues to be
addressed by the city council.
The sample is biased. The supporters may have
different ideas than those not at the rally.
B. The principal sends out questionnaires to all
of the students to find out what kind of music
students prefer at dances.
The sample is random. The students all have a chance
to respond.
7-3 Populations and Samples
Check It Out: Example 2
Determine whether each sample may be biased.
Explain.
A. The owner of a record shop surveys only
customers over the age of 18 who shop at his
store.
This is not random. Customers under the age of
18 do not have a chance of being chosen.
B. The teacher writes the name of each student on a
piece of paper and questions the students whose
names are drawn.
This sampling method is random. Each student
has an equal chance of being chosen.
7-3 Populations and Samples
Additional Example 3: Verifying Claims Based on
Statistical Data
A principal of a school with 1,500 students
estimates that about 400 students will attend
a band festival on Saturday. A random sample
of 25 students showed that 6 of them will
attend. Determine whether the principal’s
estimate is likely to be accurate.
Set up a proportion to predict the total number
of students that will attend.
Students attending sample = Students attending
# of Students sampled
Student Population
7-3 Populations and Samples
Additional Example 3 Continued
6 = x
25
1500
6 • 1500 = 25 • x
Let x represent the number of actual
students attending the band festival.
The cross products are equal.
9000 = 25x
Multiply.
9000 = 25x
25
25
Divide each side by 25 to isolate x.
360 = x
The estimate is not accurate because the data shows
that 360 students are likely to attend.
7-3 Populations and Samples
Check It Out: Example 3
The owner of a large chain restaurant with
1,200 employees estimates that about 250
employees will ask for winter vacation. A
random sample of 40 employees showed that
8 of them will ask for the time off. Determine
whether the owner’s estimate is likely to be
accurate.
Set up a proportion to predict the total number
of students that will attend.
Employees surveyed for time off = Employees asking for time off
# of Employees surveyed
Total # of Employees
7-3 Populations and Samples
Check It Out: Example 3 Continued
8 = x
40
1200
8 • 1200 = 40 • x
Let x represent the number of actual
employees asking for time off.
The cross products are equal.
9600 = 40x
Multiply.
9600 = 40x
40
40
Divide each side by 40 to isolate x.
240 = x
The estimate is accurate because the data shows that
240 employees will ask for time off.