# Mathematics III Making Inferences and Justifying Conclusions

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Understand and evaluate random processes underlying statistical experiments.
1. Understand statistics as a process for making inferences to be made about population parameters based on a random
sample from that population.
2. 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?
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
3. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how
randomization relates to each.
4. 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.
5. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between
parameters are significant.
6. Evaluate reports based on data.