# Lesson 12

Estimating a Population Mean

### Lesson Narrative

The mathematical purpose of this lesson is to estimate the population mean with an associated margin of error using sample means from random samples. The work of this lesson connects to previous work because students used sample proportions from random samples to estimate a population proportion and an associated margin of error. The work of this lesson connects to upcoming work because students will use a randomization experiment to compare two treatments. When students make connections between estimating the margin of error for population means and for population proportions they are looking for and making use of structure (MP7).

### Learning Goals

Teacher Facing

• Determine (in writing) an estimate for the population mean with a margin of error using sample means from random samples.

### Student Facing

• Let’s estimate population means using sample data.

### Required Preparation

Each student will need a number cube for the print version of the activity  Rolling for Means. Alternatively, devices that can run the GeoGebra applets are required for the digital version of this activity.

Acquire devices that can run GeoGebra (recommended) or other spreadsheet technology. It is ideal if each student has their own device. (A GeoGebra Spreadsheet is available under Math Tools.)

### Student Facing

• I can calculate the mean and standard deviation of sample means and use the information to estimate the margin of error.
• I understand that sample means that are normally distributed follow the same pattern as sample proportions.

### Glossary Entries

• margin of error

The maximum expected difference between an estimate for a population characteristic and the actual value of the population characteristic.

### Print Formatted Materials

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