# Lesson 16

Estimating Population Proportions

### Lesson Narrative

In the previous lesson, students used samples to estimate measures of center of a population. In this lesson, students estimate population proportions. The term proportion is used in statistics to refer to a number from 0 to 1 that represents the fraction of the data belonging to a given category.

Students see that if a sample is representative of the population, then we can use proportional reasoning to make predictions about the population. However, students need to understand that, due to sampling variability, these predictions are estimates, not exact answers like they get when working with actual proportional relationships (MP3).

The activity about examining a distribution of proportions from many different samples is included as an optional opportunity to deepen students' understanding of sampling variability.

### Learning Goals

Teacher Facing

• Compare (orally) proportions for the same category from different samples of a population.
• Comprehend that the term “proportion” refers to a number between 0 and 1 that represents the fraction of the data within a certain category.
• Use the proportion of a random sample that is within a certain category to make inferences about the population, and explain (orally and in writing) the reasoning.

### Student Facing

Let’s estimate population proportions using samples.

### Required Preparation

Print and cut up slips from the Reaction Times blackline master. Prepare one set of slips in a paper bag for every 2 students.

### Student Facing

• I can estimate the proportion of population data that are in a certain category based on a sample.

Building Towards

### Glossary Entries

• proportion

A proportion of a data set is the fraction of the data in a given category.

For example, a class has 18 students. There are 2 left-handed students and 16 right-handed students in the class. The proportion of students who are left-handed is $$\frac{2}{20}$$, or 0.1.

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