Statistics

Lesson 6

Math

Unit 7

7th Grade

Lesson 6 of 9

Objective


Estimate population proportions using sample data.

Common Core Standards


Core Standards

  • 7.SP.A.2 — Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Foundational Standards

  • 6.SP.B.4
  • 6.SP.B.5

Criteria for Success


  1. Find a sample proportion from a random sample of a population.
  2. Understand that there is variability in sample proportions.
  3. Use a sample proportion and a distribution of sample proportions to estimate population proportions
  4. Use estimated population proportions in situational contexts.

Tips for Teachers


  • Anchor Problem #2 is a longer activity that will take up a lot of class time. Students generate a random sample of student responses using a random number process, and they use the data from the sample to estimate information on the population (MP.4).
  • At this point in the unit, students have learned a lot of vocabulary terms. Anchor Problem #1 presents one situation and has students describe different vocabulary words within the context given. Ensure similar precision of language in the longer activity in Anchor Problem #2. 
  • Students use their proportional reasoning to estimate population quantities based on population proportions. For example, if students have an estimated population proportion, they learn that they can use proportional reasoning skills to estimate the number of people in the population with this characteristic.
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Anchor Problems


Problem 1

Akilah is running for seventh-grade class president. There are 100 students in the seventh grade at her school. To better understand her chances of winning, Akilah asks a random sample of 20 seventh graders if they plan to vote for her. In her sample, 12 out of the 20 students said they planned to vote for her. Akilah asks several friends to also ask a random sample of 20 students. Together, they combine their results to get a better understanding of her chances of winning. After winning the election, Akilah finds out that 55 out of the 100 seventh graders at her school voted for her.

Using the situation above, define and describe the following terms:

a.   sample

b.   population

c.   sample proportion

d.   population proportion

e.   sample distribution

Guiding Questions

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Problem 2

All two hundred middle school students at Roosevelt Middle School responded to several survey questions, and the results were combined in a table which your teacher will share with you.

The first column represents a unique student ID number for each student. The last column represents students’ responses to the question “Which of the following superpowers would you most like to have: invisibility, super strength, telepathy, fly, or freeze time?”

The class wants to determine the proportion of Roosevelt Middle School students who choose freeze time as their superpower.

a.   In your group, use the random number table to collect a random sample of 20 student responses to the superpower question. Record your data in a table.

b.   Determine the sample proportion for your sample.

c.   Will the other groups in your class have the same sample proportion as you? Explain your reasoning.

d.   Collect the sample proportions from the class and present the distribution in a dot plot. According to the dot plot, what is a good estimation for the population proportion? What is a good estimation for the number of students who chose freeze time as their superpower?

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 5 > Topic C > Lesson 20Teacher Version: Example 2

Grade 7 Mathematics > Module 5 > Topic C > Lesson 20 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

This diagram shows some trees in a tree farm. The circles show old trees and the triangles show young trees. Tom wants to know how many trees there are of each type, but he says it would take too long to count them all one by one. (Note, there are 50 columns and 50 rows in the diagram.)

a.   What method could he use to estimate the number of trees of each type? Explain your method fully.

b.   On the Counting Trees Worksheet, use your method to estimate the number of old trees and young trees.

Guiding Questions

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References

MARS Summative Assessment Tasks for Middle School Counting Trees

Counting Trees from the Summative Assessment Tasks for Middle School is made available through the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed March 29, 2018, 12:40 p.m..

Problem Set

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Target Task


A developer purchased an empty building on the corner of a busy intersection. She wants to open up a commercial business and is deciding between three options: coffee shop, barber shop, or deli/market.

She collects a random sample of 25 residents in the local neighborhood and asks them, “Which type of business would you prefer to have in the empty building: a coffee shop, a barber shop, or a deli/market?” Her results are shown below.

  Response   Response   Response   Response   Response
1 Deli/Market 6 Deli/Market 11 Deli/Market 16 Barber shop 21 Deli/Market
2 Coffee shop 7 Deli/Market 12 Barber shop 17 Deli/Market 22 Deli/Market
3 Deli/Market 8 Deli/Market 13 Barber shop 18 Deli/Market 23 Barber shop
4 Barber shop 9 Coffee shop 14 Deli/Market 19 Deli/Market 24 Deli/Market
5 Deli/Market 10 Coffee shop 15 Deli/Market 20 Deli/Market 25 Barber shop

a.   What is the sample proportion in favor of opening a deli/market?

b.   Estimate the population proportion in favor of opening a deli/market.

c.   If there are about 500 residents in the local neighborhood, about how many can be expected to be in favor of a deli/market?

d.   The developer decided to repeat her random sample of 25 residents several more times to ensure she had the most accurate prediction. The dot plot below shows the distribution of sample proportions. Based on the information in the dot plot, should the developer consider opening a deli/market in the empty building? Explain your reasoning. 

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 5

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Lesson 7

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Populations and Samples

Topic B: Using Sample Data to Draw Inferences About a Population

Topic C: Using Sample Data to Compare Two or More Populations

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