The mean and standard deviation.

Population percentages may be estimated when the data are approximately normally distributed.

Identify data sets as approximately normally distributed or not.

Use the mean and standard deviation of a normal distribution to estimate population percentages.

Use calculators, spreadsheets, and tables to estimate areas under the normal curve and interpret in context.

Statistics is a process for making inferences about a population based on analysis of a random sample from the population.

Identify and evaluate random sampling methods.

Explain the importance of randomness to sampling and inference making.

Explain the difference between values that describe a population and a sample, in context.

Random processes can be described mathematically by using a model: a list or description of possible outcomes.

Determine whether a given model is consistent with results from and experiment.

Know the difference between experimental and theoretical modeling.

Know how far predictions can be projected based on sample size.

Design simulations of random sampling.

Experiments must be repeated to verify a model.

Large numbers of trials can be performed using computer simulations.

Collecting data from a random sample of a population makes it possible to draw conclusions about the whole population.

Randomly assigning individuals to different treatments allows a fair comparison of the effectiveness of those treatments.

Distinguish between sample surveys, experiments, and observational studies.

Explain the importance of randomization in each of these processes.

Identify voluntary response samples and convenience samples.

Describe simple random samples, stratified random samples, and cluster samples.

Appropriately drawn samples of a population may be used to estimate a population mean or population proportion.

Relationship between margin of error, variation with a data set, and variability in the population.

Conduct simulations of random sampling to gather samples.

Estimate population means with sample means.

Estimate population proportions with sample proportions.

Calculate margins of error for the estimates.

Explain how the results relate to variability in the population.

Students may use computer generated simulation models based upon sample surveys results to estimate population statistics and margins of error.

Conduct a t-test to evaluate the effectiveness and differences in two treatments.

Use simulations to generate data simulating applying two treatments.

Use the results of simulations to determine if the differences are significant.

Read and explain, in the context of the situation, data from outside reports – discussing experimental study design, drawing conclusions from graphical and numerical summaries, and identifying characteristics of the experimental design.

Reported data may be misleading due to, for example, sample size, biased survey sample, choice of interval scale, unlabeled scale, uneven scale, and outliers.

Events are described as subsets of a sample space.

Identify a sample space, recognizing it as the set of all possible outcomes.

Identify and describe subsets of a sample space as events.

Describe unions, intersections and complements of events.

Visualize unions, intersections and complements of events with Venn diagrams.

Establish events as subsets of a sample space.

Two events A and B are independent if the probability of A and B occurring together is the product of their probabilities.

Independence of event A and event B means that the conditional probability of A given B is the same as the probability of, and the conditional probability of B given A is the same as the probability of B.

Identify events as independent or dependent.

Interpret the conditional probability of A given B as answering the question ‘now that B has occurred, what is the probability that event A will occur?

Determine the conditional probability of A given B using P(A and B)/P(B).

Represent conditional probability of A given B as P(A|B).

Calculate conditional probabilities.

Construct two-way frequency tables for two categorical variables.

Calculate probabilities from the two-way frequency table.

Use the probabilities to assess independence of two variables.

Establish events as subsets of a sample space based on union, intersection, and/or complement of other events.

Scatter plots of data sets can be used to identify the type of function that best represents the shape of the data (linear, quadratic or exponential).

Residuals (lines of regressions) are drawn on scatter plots in order to informally assess the fit of a function to a data set.

If a scatter plot has a linear association, then a line of best fit can be drawn to interpret the data set

Mutually exclusive events exist.

Analyze event B’s outcomes to determine the proportion of B’s outcomes that also belong to event A. Interpret this proportion as conditional probability of A given B.

Identify two events as mutually exclusive (disjoint).

Calculate probabilities using the Addition rule P(A or B) = P(A) + P(B) – P(A and B).