# Statistics and Probability / Comparing Populations using Sample Statistics

Grade Level 7,8
Activity 21 of 24
In this lesson, students compare two populations based on samples of the same size from each population.

## Planning and Resources

Objectives
Students make conjectures about the difference between two populations based on samples of the same size from those populations. They recognize that measures of center and spread are important in comparing means from two different populations.

Vocabulary
mean
median
interquartile range
mean absolute deviation
random sample

Standard:

## Lesson Snapshot

#### Understanding

Two simulated sampling distributions that have a small amount of variability and little overlap provide some evidence of a real difference between the two population means.

### What to look for

Investigating the distribution of the numerical difference between sample means can provide indication of a real difference between population means.

### Sample Assessment

The scores on an achievement test for 20 randomly selected boys and 20 randomly selected girls are collected. Which expressions provides some evidence that girls scored better than boys?

a) mean boys - mean girls > 0
b) mean boys - mean girls <>
c) mean boys - mean girls = 0
d) mean girls - mean boys <>

Answer: B

#### The Big Idea

Measures of center and spread are useful in comparing two random samples of the same size from different populations.

### What are the students doing?

Students use measures of center and variability from random samples to draw informal comparative inferences about two populations.

### What is the teacher doing?

Make sure students understand what the simulated sampling distribution of differences represents.