# Lesson 8 Sim City Solidify Understanding

## Learning Focus

Find an interval that is likely to contain the population proportion from a sample.

How do we know that we found the actual population proportion in a sample distribution?

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

Alyce, Javier, and Veronica continued to collect additional artifacts around the archeological site. Javier continued to look at the proportion of artifacts that are older than

### 1.

Which sectors do you believe it is possible the bag came from? Justify your response.

Alyce wonders if they could use some of their work from the other day to help make a prediction about which sector the bag of artifacts came from. She wonders if they could simulate taking samples of size

To simulate this, Alyce suggests that they assign people one of the sectors and create bags with chips that represent the proportion of artifacts older than

### 2.

Simulate taking samples of

# of artifacts of | ||||||||||
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Frequency | ||||||||||

Proportion |

# of artifacts of | ||||||||||
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Frequency | ||||||||||

Proportion |

# of artifacts of | |||||||||||
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Frequency | |||||||||||

Proportion |

Based on your simulation, do you think it is likely the dropped bag of artifacts came from your sector? Use your results to explain why you think it is or is not plausible that the bag came from your sector.

### 3.

Looking at the class distributions for the other sectors:

Are there sectors you feel confident the bag did not come from?

Which sectors do you believe the bag could have come from?

How do the graphs of the distributions provide evidence for your claim?

### 4.

One way of listing the most plausible population proportions for a sample is by using what we call a margin of error. We would list the plausible values as an interval. For example, if you thought it was plausible that the bag of artifacts came from sectors containing proportions of artifacts between

### 5.

Javier is thinking that using simulations to find an interval of plausible values takes time and wonders if their previous work on the Central Limit Theorem and sampling distributions could be useful in finding a way to create an interval of plausible values for the population proportion

#### a.

Design a strategy that you could use to find an interval of reasonable values of

#### b.

Sector 6 | Sector 5 |

Sector 4 | Sector 3 |

Sector 2 | Sector 1 |

The simulations provided show taking

### 6.

If you were to randomly sample

#### a.

How likely are you to get a sample that contains

#### b.

Based on your answer, is it likely that a bag of

## Ready for More?

What if the sample was only

## Takeaways

Margin of error:

Length of the interval**:**

## Vocabulary

- interval of plausible values
- margin of error
**Bold**terms are new in this lesson.

## Lesson Summary

In the lesson, we learned to find an interval from a sample proportion that is likely to contain the population proportion using a margin of error. To use the formula, we found the sample size must be large enough to satisfy the conditions of the Central Limit Theorem.

### 1.

Rewrite the rational expression in the form

### 2.

Find