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Colorado: AP Statistics Learning Objectives Math Standards

168 standards · 3 domains

VARIATION AND DISTRIBUTION

CB.Stats.VAR-1.A Identify questions to be answered, based on variation in one-variable data.
CB.Stats.VAR-1.B Identify variables in a set of data.
CB.Stats.VAR-1.C Classify types of variables.
CB.Stats.VAR-1.D Identify questions to be answered about possible relationships in data.
CB.Stats.VAR-1.E Identify questions to be answered about data collection methods.
CB.Stats.VAR-1.F Identify questions suggested by patterns in data.
CB.Stats.VAR-1.G Identify questions suggested by variation in statistics for samples collected from the same population.
CB.Stats.VAR-1.H Identify questions suggested by variation in the shapes of distributions of samples taken from the same population.
CB.Stats.VAR-1.I Identify questions suggested by probabilities of errors in statistical inference.
CB.Stats.VAR-1.J Identify questions suggested by variation between observed and expected counts in categorical data.
CB.Stats.VAR-1.K Identify questions suggested by variation in scatter plots.
CB.Stats.VAR-2.A Compare a data distribution to the normal distribution model.
CB.Stats.VAR-2.B Determine proportions and percentiles from a normal distribution.
CB.Stats.VAR-2.C Compare measures of relative position in data sets.
CB.Stats.VAR-3.A Identify the components of an experiment.
CB.Stats.VAR-3.B Describe elements of a well-designed experiment.
CB.Stats.VAR-3.C Compare experimental designs and methods.
CB.Stats.VAR-3.D Explain why a particular experimental design is appropriate.
CB.Stats.VAR-3.E Interpret the results of a well-designed experiment.
CB.Stats.VAR-4.A Calculate probabilities for events and their complements.
CB.Stats.VAR-4.B Interpret probabilities for events.
CB.Stats.VAR-4.C Explain why two events are (or are not) mutually exclusive.
CB.Stats.VAR-4.D Calculate conditional probabilities.
CB.Stats.VAR-4.E Calculate probabilities for independent events and for the union of two events.
CB.Stats.VAR-5.A Represent the probability distribution for a discrete random variable.
CB.Stats.VAR-5.B Interpret a probability distribution.
CB.Stats.VAR-5.C Calculate parameters for a discrete random variable.
CB.Stats.VAR-5.D Interpret parameters for a discrete random variable.
CB.Stats.VAR-5.E Calculate parameters for linear combinations of random variables.
CB.Stats.VAR-5.F Describe the effects of linear transformations of parameters of random variables.
CB.Stats.VAR-6.A Calculate the probability that a particular value lies in a given interval of a normal distribution.
CB.Stats.VAR-6.B Determine the interval associated with a given area in a normal distribution.
CB.Stats.VAR-6.C Determine the appropriateness of using the normal distribution to approximate probabilities for unknown distributions.
CB.Stats.VAR-6.D Identify the null and alternative hypotheses for a population proportion.
CB.Stats.VAR-6.E Identify an appropriate testing method for a population proportion.
CB.Stats.VAR-6.F Verify the conditions for making statistical inferences when testing a population proportion.
CB.Stats.VAR-6.G Calculate an appropriate test statistic and p-value for a population proportion.
CB.Stats.VAR-6.H Identify the null and alternative hypotheses for a difference of two population proportions.
CB.Stats.VAR-6.I Identify an appropriate testing method for the difference of two population proportions.
CB.Stats.VAR-6.J Verify the conditions for making statistical inferences when testing a difference of two population proportions.
CB.Stats.VAR-6.K Calculate an appropriate test statistic for the difference of two population proportions.
CB.Stats.VAR-7.A Describe t-distributions.
CB.Stats.VAR-7.B Identify an appropriate testing method for a population mean with unknown sigma, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.C Identify the null and alternative hypotheses for a population mean with unknown sigma, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.D Verify the conditions for the test for a population mean, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.E Calculate an appropriate test statistic for a population mean, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.F Identify an appropriate selection of a testing method for a difference of two population means.
CB.Stats.VAR-7.G Identify the null and alternative hypotheses for a difference of two population means.
CB.Stats.VAR-7.H Verify the conditions for the significance test for the difference of two population means.
CB.Stats.VAR-7.I Calculate an appropriate test statistic for a difference of two means.
CB.Stats.VAR-7.J Identify the appropriate selection of a testing method for a slope of a regression model.
CB.Stats.VAR-7.K Identify appropriate null and alternative hypotheses for a slope of a regression model.
CB.Stats.VAR-7.L Verify the conditions for the significance test for the slope of a regression model.
CB.Stats.VAR-7.M Calculate an appropriate test statistic for the slope of a regression model.
CB.Stats.VAR-8.A Describe chi-square distributions.
CB.Stats.VAR-8.B Identify the null and alternative hypotheses in a test for a distribution of proportions in a set of categorical data.
CB.Stats.VAR-8.C Identify an appropriate testing method for a distribution of proportions in a set of categorical data.
CB.Stats.VAR-8.D Calculate expected counts for the chi-square test for goodness of fit.
CB.Stats.VAR-8.E Verify the conditions for making statistical inferences when testing goodness of fit for a chi-square distribution.
CB.Stats.VAR-8.F Calculate the appropriate statistic for the chi-square test for goodness of fit.
CB.Stats.VAR-8.G Determine the p-value for the chi-square test for goodness of fit.
CB.Stats.VAR-8.H Calculate expected counts for two-way tables of categorical data.
CB.Stats.VAR-8.I Identify the null and alternative hypotheses for a chi-square test for homogeneity or independence.
CB.Stats.VAR-8.J Identify an appropriate testing method for comparing distributions in two-way tables of categorical data.
CB.Stats.VAR-8.K Verify the conditions for making statistical inferences when testing a chi-square distribution for independence or homogeneity.
CB.Stats.VAR-8.L Calculate the appropriate statistic for a chi-square test for homogeneity or independence.
CB.Stats.VAR-8.M Determine the p-value for a chi-square test for independence or homogeneity.

UNCERTAINTY AND INFERENCE

CB.Stats.UNC-1.A Represent categorical data using frequency or relative frequency tables.
CB.Stats.UNC-1.B Describe categorical data represented in frequency or relative tables.
CB.Stats.UNC-1.C Represent categorical data graphically.
CB.Stats.UNC-1.D Describe categorical data represented graphically.
CB.Stats.UNC-1.E Compare multiple sets of categorical data.
CB.Stats.UNC-1.F Classify types of quantitative variables.
CB.Stats.UNC-1.G Represent quantitative data graphically.
CB.Stats.UNC-1.H Describe the characteristics of quantitative data distributions.
CB.Stats.UNC-1.I Calculate measures of center and position for quantitative data.
CB.Stats.UNC-1.J Calculate measures of variability for quantitative data.
CB.Stats.UNC-1.K Explain the selection of a particular measure of center and/or variability for describing a set of quantitative data.
CB.Stats.UNC-1.L Represent summary statistics for quantitative data graphically.
CB.Stats.UNC-1.M Describe summary statistics of quantitative data represented graphically.
CB.Stats.UNC-1.N Compare graphical representations for multiple sets of quantitative data.
CB.Stats.UNC-1.O Compare summary statistics for multiple sets of quantitative data.
CB.Stats.UNC-1.P Compare numerical and graphical representations for two categorical variables.
CB.Stats.UNC-1.Q Calculate statistics for two categorical variables.
CB.Stats.UNC-1.R Compare statistics for two categorical variables.
CB.Stats.UNC-1.S Represent bivariate quantitative data using scatterplots.
CB.Stats.UNC-2.A Estimate probabilities using simulation.
CB.Stats.UNC-3.A Estimate probabilities of binomial random variables using data from a simulation.
CB.Stats.UNC-3.B Calculate probabilities for a binomial distribution.
CB.Stats.UNC-3.C Calculate parameters for a binomial distribution.
CB.Stats.UNC-3.D Interpret probabilities and parameters for a binomial distribution.
CB.Stats.UNC-3.E Calculate probabilities for geometric random variables.
CB.Stats.UNC-3.F Calculate parameters of a geometric distribution.
CB.Stats.UNC-3.G Interpret probabilities and parameters for a geometric distribution.
CB.Stats.UNC-3.H Estimate sampling distributions using simulation.
CB.Stats.UNC-3.I Explain why an estimator is or is not unbiased.
CB.Stats.UNC-3.J Calculate estimates for a population parameter.
CB.Stats.UNC-3.K Determine parameters of a sampling distribution for sample proportions.
CB.Stats.UNC-3.L Determine whether a sampling distribution for a sample proportion can be described as approximately normal.
CB.Stats.UNC-3.M Interpret probabilities and parameters for a sampling distribution for a sample proportion.
CB.Stats.UNC-3.N Determine parameters of a sampling distribution for a difference in sample proportions.
CB.Stats.UNC-3.O Determine whether a sampling distribution for a difference of sample proportions can be described as approximately normal.
CB.Stats.UNC-3.P Interpret probabilities and parameters for a sampling distribution for a difference in proportions.
CB.Stats.UNC-3.Q Determine parameters of a sampling distribution for a sample mean.
CB.Stats.UNC-3.R Determine whether a sampling distribution of a sample mean can be described as approximately normal.
CB.Stats.UNC-3.S Interpret probabilities and parameters for a sampling distribution for a sample mean.
CB.Stats.UNC-3.T Determine parameters of a sampling distribution for a difference in sample means.
CB.Stats.UNC-3.U Determine whether a sampling distribution of a difference in sample means can be described as approximately normal.
CB.Stats.UNC-3.V Interpret probabilities and parameters for a sampling distribution for a difference in sample means.
CB.Stats.UNC-4.A Identify an appropriate confidence interval procedure for a population proportion.
CB.Stats.UNC-4.B Verify the conditions for calculating confidence intervals for a population proportion.
CB.Stats.UNC-4.C Determine the margin of error for a given sample size and an estimate for the sample size that will result in a given margin of error for a population proportion.
CB.Stats.UNC-4.D Calculate an appropriate confidence interval for a population proportion.
CB.Stats.UNC-4.E Calculate an interval estimate based on a confidence interval for a population proportion.
CB.Stats.UNC-4.F Interpret a confidence interval for a population proportion.
CB.Stats.UNC-4.G Justify a claim based on a confidence interval for a population proportion.
CB.Stats.UNC-4.H Identify the relationships between sample size, width of a confidence interval, confidence level, and margin of error for a population proportion.
CB.Stats.UNC-4.I Identify an appropriate confidence interval procedure for a comparison of population proportions.
CB.Stats.UNC-4.J Verify the conditions for calculating confidence intervals for a difference between population proportions.
CB.Stats.UNC-4.K Calculate an appropriate confidence interval for a comparison of population proportions.
CB.Stats.UNC-4.L Calculate an interval estimate based on a confidence interval for a difference of proportions.
CB.Stats.UNC-4.M Interpret a confidence interval for a difference of proportions.
CB.Stats.UNC-4.N Justify a claim based on a confidence interval for a difference of proportions.
CB.Stats.UNC-4.O Identify an appropriate confidence interval procedure for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.P Verify the conditions for calculating confidence intervals for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.Q Determine the margin of error for a given sample size for a one-sample t-interval.
CB.Stats.UNC-4.R Calculate an appropriate confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.S Interpret a confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.T Justify a claim based on a confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.U Identify the relationships between sample size, width of a confidence interval, confidence level, and margin of error for a population mean.
CB.Stats.UNC-4.V Identify an appropriate confidence interval procedure for a difference of two population means.
CB.Stats.UNC-4.W Verify the conditions for calculating confidence intervals for the difference of two population means.
CB.Stats.UNC-4.X Determine the margin of error for the difference of two population means.
CB.Stats.UNC-4.Y Calculate an appropriate confidence interval for a difference of two population means.
CB.Stats.UNC-4.Z Interpret a confidence interval for a difference of population means.
CB.Stats.UNC-5.A Identify Type I and Type II errors.
CB.Stats.UNC-5.B Calculate the probability of a Type I and Type II errors.
CB.Stats.UNC-5.C Identify factors that affect the probability of errors in significance testing.
CB.Stats.UNC-5.D Interpret Type I and Type II errors.

DATA ANALYSIS

CB.Stats.DAT-1.A Describe the characteristics of a scatter plot.
CB.Stats.DAT-1.B Determine the correlation for a linear relationship.
CB.Stats.DAT-1.C Interpret the correlation for a linear relationship.
CB.Stats.DAT-1.D Calculate a predicted response value using a linear regression model.
CB.Stats.DAT-1.E Represent differences between measured and predicted responses using residual plots.
CB.Stats.DAT-1.F Describe the form of association of bivariate data using residual plots.
CB.Stats.DAT-1.G Estimate parameters for the least-squares regression line model.
CB.Stats.DAT-1.H Interpret coefficients for the least-squares regression line model.
CB.Stats.DAT-1.I Identify influential points in regression.
CB.Stats.DAT-1.J Calculate a predicted response using a least-squares regression line for a transformed data set.
CB.Stats.DAT-2.A Identify the type of a study.
CB.Stats.DAT-2.B Identify appropriate generalizations and determinations based on observational studies.
CB.Stats.DAT-2.C Identify a sampling method, given a description of a study.
CB.Stats.DAT-2.D Explain why a particular sampling method is or is not appropriate for a given situation.
CB.Stats.DAT-2.E Identify potential sources of bias in sampling methods.
CB.Stats.DAT-3.A Interpret the p-value of a significance test for a population proportion.
CB.Stats.DAT-3.B Justify a claim about the population based on the results of a significance test for a population proportion.
CB.Stats.DAT-3.C Interpret the p-value of a significance test for a difference of population proportions.
CB.Stats.DAT-3.D Justify a claim about the population based on the results of a significance test for a difference of population proportions.
CB.Stats.DAT-3.E Interpret the p-value of a significance test for a population mean, including the mean difference between values in matched pairs.
CB.Stats.DAT-3.F Justify a claim about the population based on the results of a significance test for a population mean.
CB.Stats.DAT-3.G Interpret the p-value of a significance test for a difference of population means.
CB.Stats.DAT-3.H Justify a claim about the population based on the results of a significance test for a difference of two population means in context.
CB.Stats.DAT-3.I Interpret the p-value for the chi-square test for goodness of fit.
CB.Stats.DAT-3.J Justify a claim about the population based on the results of a chi-square test for goodness of fit.
CB.Stats.DAT-3.K Interpret the p-value for the chi-square test for homogeneity or independence.
CB.Stats.DAT-3.L Justify a claim about the population based on the results of a chi-square test for homogeneity or independence.
CB.Stats.DAT-3.M Interpret the p-value of a significance test for the slope of a regression model.
CB.Stats.DAT-3.N Justify a claim about the population based on the results of a significance test for the slope of a regression model.