Lesson 8.2.1 – Teacher Notes
Standard:
7.SP.A.1 Understand that statistics can be used to gain information about a population by
examining a sample of the population; generalizations about a population from a sample are
valid only if the sample is representative of that population. Understand that random
sampling tends to produce representative samples and support valid inferences.
• Full mastery can be expected by the end of the chapter.
Lesson Focus:
The focus of the lesson is to have students critique the validity of data based on the sample
surveyed. Problem 8-30 may be skipped as it includes additional vocabulary which may not be
needed and therefore may be overwhelming. (8-29 and 8-31)
• I can generalize that random sampling tends to produce representative samples and
support valid inferences.
Calculator: Yes
Literacy/Teaching Strategy: Think-Pair-Share (8-29)
Bell Work
If you want to know what a bowl of soup tastes like, do you
need to eat all of the soup in the bowl? Or can you get a
good idea of the taste by trying a small sample?
When you conduct a survey, it is not usually possible for you
to survey every person in the population you are interested
in, such as all female teenage shoppers or all of the
students at your school. Instead, statisticians collect
information about a sample (a portion) of the
population. However, finding a representative sample (a
sample that represents the whole population well) is not
easy.
8-29. As the social director of the
Class Council, Heather would like to
survey a few students about their
interests.
When Heather analyzes the
results from the survey, she wants to
make claims about the interests of all of the students in her
school. If he were to survey only students on the Class
Council, for example, it might be hard to make claims about
what all students think. Students who are on the Class Council
may not have the same social interests as other
students. Consider this idea as you think about the samples
described below.
a. If Heather wanted to generalize the opinions of all
students at his school, would it make sense to go to
the grocery store and survey the people there? Why
or why not?
8-29. As the social director of the
Class Council, Heather would like to
survey a few students about their
interests.
When Heather analyzes the
results from the survey, she wants to
make claims about the interests of all of the students in her
school. If he were to survey only students on the Class
Council, for example, it might be hard to make claims about
what all students think. Students who are on the Class Council
may not have the same social interests as other
students. Consider this idea as you think about the samples
described below.
b. If she wanted to generalize the opinions of all
students at her school, would it make sense to ask all
of her friends at school? Why or why not?
8-29. As the social director of the
Class Council, Heather would like to
survey a few students about their
interests.
When Heather analyzes the
results from the survey, she wants to
make claims about the interests of all of the students in her
school. If he were to survey only students on the Class
Council, for example, it might be hard to make claims about
what all students think. Students who are on the Class Council
may not have the same social interests as other
students. Consider this idea as you think about the samples
described below.
c. If he wanted to generalize the opinions of all students at
his school, would it make sense to ask every third
person who entered the cafeteria at lunch? Why or why
not?
8-31. From what population is each of these samples
taken? Write down the actual population for each of these
sampling techniques.
8-32. A study at the University of Iowa in 2008 concluded
that children that play violent video games are more
aggressive in real life. Children ages 9 to 12 were studied
to determine how much they played violent video games;
peers and teachers were asked how much these students
hit, kicked, and got into fights with other students.
a. Can you legitimately conclude from this study that
teenagers who play violent video games tend to be more
aggressive? Why or why not?
8-32. A study at the University of Iowa in 2008 concluded
that children that play violent video games are more
aggressive in real life. Children ages 9 to 12 were studied
to determine how much they played violent video games;
peers and teachers were asked how much these students
hit, kicked, and got into fights with other students.
b. Can you legitimately conclude from this study that
children ages 9 to 12 who play violent video games are
more likely to commit violent crimes? Why or why
not?
8-32. A study at the University of Iowa in 2008 concluded
that children that play violent video games are more
aggressive in real life. Children ages 9 to 12 were studied
to determine how much they played violent video games;
peers and teachers were asked how much these students
hit, kicked, and got into fights with other students.
c. Can you legitimately conclude from this study that
children ages 9 to 12 who play violent video games tend
to hit and kick more in school?
8-32. A study at the University of Iowa in 2008 concluded
that children that play violent video games are more
aggressive in real life. Children ages 9 to 12 were studied
to determine how much they played violent video games;
peers and teachers were asked how much these students
hit, kicked, and got into fights with other students.
d. Can you legitimately conclude from this study that
playing a lot of violent video games will cause 9 to 12year-old students to become more violent at school?
Practice
Determine if each sample is valid. If it is not, give a
suggestion to make it valid.
1. A marketing person for a company that manufactures
roller coaster reports that 92% of Americans like to ride
roller coasters. She based this on the data collected from
a survey that was given to people who visited American
amusement parks over the course of the summer.
2. The school newspaper reports that 47% of seventh
graders at the school have at least two siblings. This is
based on data that a student gathered from his 3rd period
class.
Practice
3. Give at least one pro and one con for each sampling method. Then
state which method is best.
Snacks Stat! is considering introducing a new chip, Seeds ‘n’
Stuff. Your Manager of Surveys has suggested the following
four methods for selecting a sample to determine customer
demand for this product in the town of 1,500 people:
Method A: Survey the first 25 people in line on a weekday for
the noon showing of Monster Mayhem at the local movie
theater.
Method B: Survey every 5th person arriving at the local
playground on a weekday afternoon until 25 people are
questioned.
Method C: Randomly select 5 citizens from records at town
hall. Contact each person and arrange to survey him or her.
Method D: Randomly select 50 citizens from records at town
hall. Contact each person and arrange to survey him or her.