[MA2015] (7) 18 :
18 ) Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7-SP2]
Example: Estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
[MA2015] PRE (9-12) 45 :
45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]
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'
[MA2015] PRE (9-12) 46 :
46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]
[MA2015] PRE (9-12) 48 :
48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]
[MA2015] PRE (9-12) 49 :
49 ) Evaluate reports based on data. [S-IC6]
[MA2019] REG-7 (7) 10 :
10. Examine a sample of a population to generalize information about the population.
a. Differentiate between a sample and a population.
b. Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.
c. Determine whether conclusions and generalizations can be made about a population based on a sample.
d. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.
e. Informally explain situations in which statistical bias may exist. [MA2019] REG-7 (7) 12 :
12. Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.