16 Questions
What is the main objective of the librarian in collecting the age data of the children's section patrons?
To select age-appropriate activities for the children
What is the assumption made when using a sample to make inferences about a population?
The sample is representative of the population
What is the purpose of a dot plot in this context?
To visualize the sample population data
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
What can be used to make inferences or predictions about the population?
Data based on a random sample and proportional reasoning
What is the term for using data based on a random sample to make inferences or predictions about the population?
Inferential statistics
What is the purpose of checking seatwork and having a discussion in this lesson?
To assess the students' understanding of the concept
What is the purpose of making a box plot of the sample population data?
To visualize the distribution of the sample population data
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
In Example 1, what is the probability that an MP3 player is defective?
3/50
How many tickets are likely to have been purchased on the first day in Example 2?
448
What is the purpose of using proportional reasoning in these examples?
To make an educated estimate about the population based on the sample
In the seatwork, how many elk are likely to be infected with the parasite?
720
What is the sample size in the seatwork question about smartphones?
60
Can random samples and proportional reasoning provide precise information about a population?
No, but they can provide an estimate
What is the advantage of using a random sample?
It allows for proportional reasoning to make an estimate about the population
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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