Making Inferences and Justifying Conclusions
Understand and evaluate random processes underlying statistical experiments
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Statistics
Population Inferences
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2 - Understand (statistics as a process for making inferences about population parameters based on a random sample from that population)
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2 - I can understand statistics as a process for making inferences about population parameters based on a random sample from that population.
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A. Statistics is the process used for making inferences about a population’s parameters based on a random sample from that population.
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A.1 What is a population?
A.2 What is a population parameter?
A.3 What is a random sample?
A.4 How can a random sample from a population be the basis for statistical inference about the population’s parameters?
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Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Model
Data-Generating Process
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3 - Use (simulation of model)
1 - Generate (data)
5 - Decide (if model is consistent with results from data-generating process or simulation)
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3 - I can use simulation to
1 - I can generate data.
5 - I can decide if a specified model is consistent with results from a given data generating process or simulation.
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A. The results of a specified model can be evaluated for consistency by the use of a data-generating process or simulation.
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A.1 How can a specific model be simulated?
A.2 How can the consistency of a specific model be evaluated when compared to the results of a simulation?
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Make inferences and justify conclusions from sample surveys, experiments, and observational studies
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Data collection Methods
Characteristics
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2 - Recognize (purposes of sample surveys, experiments, and observational studies)
2 - Recognize (differences among sample surveys, experiments, and observational studies)
4 - Explain (how randomization relates to sample surveys, experiments, and observational studies)
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2 - I can recognize the purposes of sample surveys, experiments, and observational studies.
2 - I can recognize the differences among sample surveys, experiments, and observational studies.
4 - I can explain how randomization relates to sample surveys, experiments, and observational studies.
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A. Methods of data collection include sample surveys, experiments, and observational studies, each of which can be used for a specific purpose.
B. Sample surveys, experiments, and observational studies are designed and conducted by different methods.
C. The use of randomization in the design of sample surveys, experiments, and observational studies can have an effect on the results.
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A.1 How is the design of a sample survey related to its purpose?
A.2 How is the design of an experiment related to its purpose?
A.3 How is the design of an observational study related to its purpose?
B.1 What are the differences among sample surveys, experiments, and observational studies?
C.1 What role does randomization play in the design of sample surveys, experiments, and observational studies?
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Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Sample survey
Margin of error
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3 - Use (data from a sample survey)
3 - Estimate (a population mean or proportion)
5 - Develop (margin of error)
3 - Use (simulation model)
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3 - I can use data from a sample survey.
3 - I can estimate a population mean or proportion.
5 - I can develop a margin of error.
3 - I can use a simulation model for random sampling.
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A. Data collected from a sample survey can be used to estimate a population mean or proportion.
B. Data collected by the use of simulation models for random sampling can be used to develop a margin of error.
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A.1 What is a population mean?
A.2 What is a population proportion?
A.3 How can data from a sample survey be used to estimate a population mean or proportion?
B.1 What is a margin of error?
B.2 How can data collected from simulation models for random sampling be used to develop a margin of error?
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Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Parameters
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3 - Use (data from randomized experiments)
4 - Compare (two treatments)
3 - Use (simulations)
5 - Decide (if differences between parameters are significant)
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4 - I can use data from a randomized experiment.
2 - I can compare two treatments.
5 - I can use simulations.
5 - I can decide if differences between parameters are significant.
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A. Data collected from a randomized experiment can be used to compare two treatments.
B. Data collected from simulations can be used to decide if differences between parameters are significant.
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A.1 How can the data from a randomized experiment be used to compare two treatments?
B.1 What is the meaning of significant differences (between parameters)?
B.2 How can data collected from simulations be used to decide if significant differences exist between parameters?
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Evaluate reports based on data.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Reports
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5 - Evaluate (reports based on data)
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5 - I can evaluate reports based on data.
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A. Reports based on data can be evaluated for a variety of characteristics.
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A.1 Why should reports based on data be evaluated?
A.2 By what methods can reports based on data be evaluated?
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