Proportions and Inferences

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Questions and Answers

What is the main objective of the librarian in collecting the age data of the children's section patrons?

To determine the range of ages of children using the library

To select age-appropriate activities for the children (correct)

To identify the most common age of children using the library

To create a dot plot of the sample population data

What is the assumption made when using a sample to make inferences about a population?

The sample is representative of the population (correct)

The sample is biased towards a specific age group

The sample is larger than the population

The sample is randomly selected

What is the purpose of a dot plot in this context?

To make predictions about the population

To visualize the sample population data (correct)

To identify the most common age of children using the library

To show the range of ages of children using the library

What is proportional to the number of objects in the sample with a given characteristic?

The number of objects in the population with that characteristic Signup and view all the answers

What can be used to make inferences or predictions about the population?

Data based on a random sample and proportional reasoning Signup and view all the answers

What is the term for using data based on a random sample to make inferences or predictions about the population?

Inferential statistics Signup and view all the answers

What is the purpose of checking seatwork and having a discussion in this lesson?

To assess the students' understanding of the concept Signup and view all the answers

What is the purpose of making a box plot of the sample population data?

To visualize the distribution of the sample population data Signup and view all the answers

What is the purpose of selecting a random sample in the given examples?

To make an educated estimate about the population based on the sample Signup and view all the answers

In Example 1, what is the probability that an MP3 player is defective?

3/50 Signup and view all the answers

How many tickets are likely to have been purchased on the first day in Example 2?

448 Signup and view all the answers

What is the purpose of using proportional reasoning in these examples?

To make an educated estimate about the population based on the sample Signup and view all the answers

In the seatwork, how many elk are likely to be infected with the parasite?

720 Signup and view all the answers

What is the sample size in the seatwork question about smartphones?

60 Signup and view all the answers

Can random samples and proportional reasoning provide precise information about a population?

No, but they can provide an estimate Signup and view all the answers

What is the advantage of using a random sample?

It allows for proportional reasoning to make an estimate about the population Signup and view all the answers

Study Notes

Proportions to Make Inferences

A sample is representative of the population if it has the same characteristics as the population.
Proportional reasoning can be used to make inferences or predictions about the population based on a random sample.

Examples of Making Inferences

A shipment of 3,500 MP3 players has a random sample of 50, with 3 defective players, so the number of defective players in the shipment is likely to be proportional to the sample.
A concert with 4,200 seats has a random sample of 120 ticket buyers, with 28 buyers making their purchase on the first day, so the number of tickets purchased on the first day is likely to be proportional to the sample.

Seatwork Examples

A manufacturer fills an order for 4,200 smartphones, with a random sample of 60 phones showing 4 defective phones, so the number of defective phones in the order is likely to be proportional to the sample.
A random sample of 50 elk from a population of 4,500 elk shows that 8 are infected with a parasite, so the number of elk infected with the parasite is likely to be proportional to the sample.

Limitations of Proportional Reasoning

Random samples and proportional reasoning cannot be used to determine precise information about a population.
Proportional reasoning is used to make inferences or predictions, but it is not exact.

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