# Lesson 8 Ancient Treasures Solidify Understanding

## Learning Focus

Use random sampling methods and find means and proportions for random samples.

How do researchers find averages and percentages for a population when they can’t measure the entire population?

## Open Up the Math: Launch, Explore, Discuss

Alyce, Javier, and Veronica have made a significant amount of progress at the archeological site after staking it out. They have been slowly uncovering artifacts in the different sectors and have a collection of

A list of the artifacts and their age is given in a table, and a histogram of the data is shown here:

### 1.

What observations do you have about the artifacts based on the data set and the histogram? What questions might you ask about the data?

As Alyce is looking at the data, she is wondering about two questions: What is the average age of the artifacts, and what proportion of these artifacts are over

### 2.

#### a.

Select and describe a sampling method you could use to select a random sample of

#### b.

Using your sampling method, randomly select a sample of

#### c.

Based on your sample, make a prediction for the actual average age of all the artifacts.

### 3.

To help the archeologists, take

Average Age | Proportion of Artifacts Older than | |
---|---|---|

Sample 1 | ||

Sample 2 | ||

Sample 3 |

As Alyce looks at the graph created, she notices that it looks a little different from the graph of the original

### 4.

Compare this new graph with the graph for the population of all

### 5.

Explain the difference between how this new graph was created and how the graph for the

Pause and Reflect

As Veronica is looking at the graphs, she is still wondering about using only

### 6.

Take

Average Age | Proportion of Artifacts Older than | |
---|---|---|

Sample 1 | ||

Sample 2 | ||

Sample 3 |

Average Age | Proportion of Artifacts Older than | |
---|---|---|

Sample 1 | ||

Sample 2 | ||

Sample 3 |

### 7.

Compare and contrast the distributions of these graphs with the original and write your observations.

Pause and Reflect

### 8.

If you were to take one sample and use that one sample to predict the average age of all

## Ready for More?

Give an example where it might be nearly impossible to find the population mean, but it would be possible to take random samples to find a sample mean.

## Takeaways

Central Limit Theorem:

Given a population with mean

## Adding Notation, Vocabulary, and Conventions

Parameter:

Population mean:

Population proportion:

Sample statistic:

Sample mean:

Sample proportion:

## Vocabulary

- Central Limit Theorem (CLT)
- inference (statistics)
- parameter
- population mean
- population proportion
- sample mean
- sample proportion
- sample statistic
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we sampled a population and used the mean and proportion of the population to estimate the actual mean and proportion of the population, which are called population parameters. We learned about the Central Limit Theorem, which says that if the sample is large enough, the sample means and proportions will be normally distributed.

### 1.

Find the polynomial quotient and the remainder. Then indicate whether the binomial is a factor of the polynomial.

### 2.

Given: