AP Stats

From the CollegeBoard.org: “AP Statistics is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem solving, and writing as they explore concepts like variation and distribution; patterns and uncertainty; and data-based predictions, decisions, and conclusions.”

This course is designed to prepare students for the AP Statistics Exam, a 3-hour proctored test facilitated by the College Board. Successful completion of AP Exams can earn college credit and the opportunity to skip introductory courses in college (credit policies vary by school). At the very least, taking this class gives students the chance to preview college-level work in a familiar setting.

Learning Objectives: Students will be able to...

• Identify the individuals and variables in a set of data.

• Classify variables as categorical or quantitative.

• Display categorical data with a bar graph. Decide whether it would be appropriate to make a pie chart.

• Identify what makes some graphs of categorical data deceptive.

• Calculate and display the marginal distribution of a categorical variable from a two-way table.

• Calculate and display the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table.

• Describe the association between two categorical variables by comparing appropriate conditional distributions.

• Make and interpret dotplots and stemplots.

• Describe a distribution (SOCS).

• Identify the shape of a distribution from a graph as roughly symmetric or skewed.

• Make and interpret histograms.

• Compare distributions of quantitative data using dotplots, stemplots, or histograms.

• Calculate measures of center (mean, median).

• Calculate and interpret measures of spread (range, IQR, standard deviation).

• Choose the most appropriate measure of center and spread in a given setting.

• Identify outliers using the 1.5 × IQR rule.

• Make and interpret boxplots.

• Use appropriate graphs and numerical summaries to compare distributions of quantitative variables.

Learning Objectives: Students will be able to...

• Find and interpret the percentile of an individual value within a distribution of data.

• Estimate percentiles and individual values using a cumulative relative frequency graph.

• Find and interpret the standardized score (z-score) of an individual within a distribution of data.

• Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and spread of a distribution of data.

• Estimate the relative locations of the median and mean on a density curve.

• Estimate areas (proportions of values) in a Normal distribution.

• Find the proportion of z-values in a specified interval, or a z-score from a percentile in the standard Normal distribution.

• Find the proportion of values in a specified interval, or the value that corresponds to a given percentile in any Normal distribution.

• Determine whether a distribution of data is approximately Normal from graphical and numerical evidence.

Learning Objectives: Students will be able to...

• Identify explanatory and response variables in situations where one variable helps to explain or influence the other.

• Make a scatterplot to display the relationship between two quantitative variables.

• Describe the direction, form, and strength of a relationship displayed in a scatterplot and identify outliers in a scatterplot.

• Interpret the correlation.

• Understand the basic properties of a correlation, including how the correlation is influenced by outliers.

• Use technology to calculate correlation.

• Explain why association does not imply causation.

• Interpret the slope and y-intercept of a least-squares regression line (LSRL).

• Use the LSRL to predict y given x.

• Calculate and interpret residuals and their standard deviation.

• Explain the concept of least squares.

• Determine the equation of a LSRL using a variety of methods.

• Construct and interpret residual plots to assess whether a linear model is appropriate.

• Assess how well the LSRL models the relationship between two variables.

• Describe how the slope, y-intercept, standard deviation of the residuals, and r2 are influenced by outliers. 

Learning Objectives: Students will be able to...

• Identify the population and sample in a statistical study.

• Identify voluntary response samples and convenience samples. Explain how these sampling methods can lead to bias.

• Describe how to obtain a random sample using slips of paper, technology, or a table of random digits.

• Distinguish a simple random sample from a stratified random sample or cluster sample. Give the advantages and disadvantages of each sampling method.

• Explain how undercoverage, nonresponse, question wording, and other aspects of a sample survey can lead to bias.

• Distinguish between an observational study and an experiment.

• Explain the concept of confounding.

• Identify the experimental units, explanatory and response variables, and treatments in an experiment.

• Describe a completely randomized design for an experiment.

• Describe the placebo effect and the purpose of blinding in an experiment.

• Interpret the meaning of statistically significant in the context of an experiment.

• Explain the purpose of blocking in an experiment. Describe a randomized block design or a matched pairs design for an experiment.

• Describe the scope of inference that is appropriate.

• Evaluate whether a statistical study has been carried out in an ethical way.

Learning Objectives: Students will be able to...

• Interpret probability as a long-run relative frequency.

• Use simulation to model chance behavior.

• Determine a probability model for a chance process.

• Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.

• Use a two-way table or Venn diagram to model a chance process and calculate probabilities involving two events.

• Use the general addition rule to calculate probabilities.

• Calculate and interpret conditional probabilities.

• Use the general multiplication rule to calculate probabilities.

• Use tree diagrams to model a chance process and calculate probabilities involving two or more events.

• Determine whether two events are independent.

• When appropriate, use the multiplication rule for independent events to compute probabilities.

Learning Objectives: Students will be able to...

• Compute probabilities using the probability distribution of a discrete random variable.

• Calculate and interpret the mean (expected value) of a discrete random variable.

• Calculate and interpret the standard deviation of a discrete random variable.

• Compute probabilities using the probability distribution of certain continuous random variables.

• Describe the effects of transforming a random variable by adding or subtracting a constant and multiplying or dividing by a constant.

• Find the mean and standard deviation of the sum or difference of independent random variables.

• Find probabilities involving the sum or difference of independent Normal random variables.

• Determine whether the conditions for using a binomial random variable are met.

• Compute and interpret probabilities involving binomial distributions.

• Calculate the mean and standard deviation of a binomial random variable. Interpret these values in context.

• Find probabilities involving geometric random variables.

• When appropriate, use the Normal approximation to the binomial distribution to calculate probabilities.

Learning Objectives: Students will be able to...

• Distinguish between a parameter and a statistic.

• Use the sampling distribution of a statistic to evaluate a claim about a parameter.

• Distinguish among the distribution of a population, the distribution of a sample, and the sampling distribution of a statistic.

• Determine whether or not a statistic is an unbiased estimator of a population parameter.

• Describe the relationship between sample size and the variability of a statistic.

• Find the mean and standard deviation of the sampling distribution of a sample proportion. Check the 10% condition.

• Determine if the sampling distribution of a sample proportion is approximately Normal.

• If appropriate, use a Normal distribution to calculate probabilities involving sample proportion.

• Find the mean and standard deviation of the sampling distribution of a sample mean. Check the 10% condition.

• Explain how the shape of the sampling distribution of a sample mean is affected by the shape of the population distribution and the sample size.

• If appropriate, use a Normal distribution to calculate probabilities involving sample mean.

Learning Objectives: Students will be able to...

• Determine the point estimate and margin of error from a confidence interval.

• Interpret a confidence interval in context.

• Interpret a confidence level in context.

• Describe how the sample size and confidence level affect the length of a confidence interval.

• Explain how practical issues like nonresponse, undercoverage, and response bias can affect the interpretation of a confidence interval.

• State and check the Random, 10%, and Large Counts conditions for constructing a confidence interval for a population proportion.

• Determine critical values for calculating a C% confidence interval for a population proportion using a table or technology.

• Construct and interpret a confidence interval for a population proportion.

• Determine the sample size required to obtain a C% confidence interval for a population proportion with a specified margin of error.

• State and check the Random, 10%, and Normal/Large Sample conditions for constructing a confidence interval for a population mean.

• Explain how the t distributions are different from the standard Normal distribution and why it is necessary to use a t distribution when calculating a confidence interval for a population mean.

• Determine critical values for calculating a C% confidence interval for a population mean using a table or technology.

• Construct and interpret a confidence interval for a population mean.

• Determine the sample size required to obtain a C% confidence interval for a population mean with a specified margin of error. 

Learning Objectives: Students will be able to...

• State the null and alternative hypotheses for a significance test about a population parameter.

• Interpret a P-value in context.

• Determine if the results of a study are statistically significant and draw an appropriate conclusion using a significance level.

• Interpret a Type I and a Type II error in context, and give a consequence of each.

• State and check the Random, 10%, and Large Counts conditions for performing a significance test about a population proportion.

• Perform a significance test about a population proportion.

• Interpret the power of a test and describe what factors affect the power of a test.

• Describe the relationship among the probability of a Type I error (significance level), the probability of a Type II error, and the power of a test.

• State and check the Random, 10%, and Normal/Large Sample conditions for performing a significance test about a population mean.

• Perform a significance test about a population mean.

• Use a confidence interval to draw a conclusion for a two-sided test about a population parameter.

• Perform a significance test about a mean difference using paired data.

Learning Objectives: Students will be able to...

• Describe the shape, center, and spread of the sampling distribution of the difference of two sample proportions.

• Determine whether the conditions are met for doing inference about p1 − p2.

• Construct and interpret a confidence interval to compare two proportions.

• Perform a significance test to compare two proportions.

• Describe the shape, center, and spread of the sampling distribution of the difference of two sample means.

• Determine whether the conditions are met for doing inference about µ1 − µ2.

• Construct and interpret a confidence interval to compare two means.

• Perform a significance test to compare two means.

• Determine when it is appropriate to use two-sample t procedures versus paired t procedures.

Learning Objectives: Students will be able to...

• State appropriate hypotheses and compute expected counts for a chi-square test for goodness of fit.

• Calculate the chi-square statistic, degrees of freedom, and P-value for a chi-square test for goodness of fit.

• Perform a chi-square test for goodness of fit.

• Conduct a follow-up analysis when the results of a chi-square test are statistically significant.

• Compare conditional distributions for data in a two-way table.

• State appropriate hypotheses and compute expected counts for a chi-square test based on data in a two-way table.

• Calculate the chi-square statistic, degrees of freedom, and P-value for a chi-square test based on data in a two-way table.

• Perform a chi-square test for homogeneity. 

• Perform a chi-square test for independence. 

• Choose the appropriate chi-square test.

Learning Objectives: Students will be able to...

• Check the conditions for performing inference about the slope β of the population (true) regression line.

• Interpret the values of a, b, s, SEb , and r2 in context, and determine these values from computer output.

• Construct and interpret a confidence interval for the slope β of the population (true) regression line. 

• Perform a significance test about the slope β of the population (true) regression line.

• Use transformations involving powers and roots to find a power model that describes the relationship between two variables, and use the model to make predictions.

• Use transformations involving logarithms to find a power model or an exponential model that describes the relationship between two variables, and use the model to make predictions.

• Determine which of several transformations does a better job of producing a linear relationship.