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Skills available for Alabama Algebra 2 standards

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AII.NQ Number and Quantity

AII.AF Algebra and Functions

AII.DSP Data Analysis, Statistics, and Probability

  • Focus 1: Quantitative Literacy

    • Mathematical and statistical reasoning about data can be used to evaluate conclusions and assess risks.

      • 23 Use mathematical and statistical reasoning about normal distributions to draw conclusions and assess risk; limit to informal arguments.

    • Making and defending informed data-based decisions is a characteristic of a quantitatively literate person.

  • Focus 2: Visualizing and Summarizing Data

    • Distributions of quantitative data (continuous or discrete) in one variable should be described in the context of the data with respect to what is typical (the shape, with appropriate measures of center and variability, including standard deviation) and what is not (outliers), and these characteristics can be used to compare two or more subgroups with respect to a variable.

  • Focus 3: Statistical Inference

    • Study designs are of three main types: sample survey, experiment, and observational study.

      • 26 Describe the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

    • The role of randomization is different in randomly selecting samples and in randomly assigning subjects to experimental treatment groups.

      • 27 Distinguish between a statistic and a parameter and use statistical processes to make inferences about population parameters based on statistics from random samples from that population.

      • 28 Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect.

    • The scope and validity of statistical inferences are dependent on the role of randomization in the study design.

      • 29 Explain the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experiments.

    • Bias, such as sampling, response, or nonresponse bias, may occur in surveys, yielding results that are not representative of the population of interest.

      • 30 Evaluate where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are representative of the population of interest.

    • The larger the sample size, the less the expected variability in the sampling distribution of a sample statistic.

      • 31 Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic.

        • 31.a Simulate a sampling distribution of sample means from a population with a known distribution, observing the effect of the sample size on the variability.

        • 31.b Demonstrate that the standard deviation of each simulated sampling distribution is the known standard deviation of the population divided by the square root of the sample size.

    • The sampling distribution of a sample statistic formed from repeated samples for a given sample size drawn from a population can be used to identify typical behavior for that statistic. Examining several such sampling distributions leads to estimating a set of plausible values for the population parameter, using the margin of error as a measure that describes the sampling variability.

      • 32 Produce a sampling distribution by repeatedly selecting samples of the same size from a given population or from a population simulated by bootstrapping (resampling with replacement from an observed sample). Do initial examples by hand, then use technology to generate a large number of samples.

      • 33 Use data from a randomized experiment to compare two treatments; limit to informal use of simulations to decide if an observed difference in the responses of the two treatment groups is unlikely to have occurred due to randomization alone, thus implying that the difference between the treatment groups is meaningful.

AII.GM Geometry and Measurement