Graphical displays of distributions of univariate data: dotplots, stem-and-leaf plots,
histograms (Center and spread, Clusters and gaps, Outliers and other unusual features, Shape and skewness); Summarizing distributions of univariate data (Measuring central tendency -- mean, median, mode, Measuring spread -- range, interquartile range, standard deviation, Measuring position -- quartiles, percentiles, Box-and-whiskers plots, Changing units and standardizing scores); Comparing distributions of univariate data (dotplots, back-to-back stem-and-leaf plots, parallel box-and-whiskers plots)

Gaining specific facts, ideas, vocabulary;Reading a variety of sources for information and pleasure; comprehending what has been read; making inferences and drawing conclusions; sorting and categorizing information; arranging into understandable forms, such as narrative descriptions, tables, timelines, graphs and diagrams; interpreting data; drawing conclusions from relationships and patterns which emergefrom organized data. communicating what has been learned.

Normal distribution:
* Properties
* Using normal probability tables
* Using as a model for measurements
* Assessing normality

1. locate median and mean on a density curve.
2. recognize symmetric, left-skew, and right-skew distributions.
3. Use the Empirical Rule
3. compute the standardized vale of an observation.
4. use the table or the calculator to calculate the proportion of values above (or below) a stated number.
5. calculate a point having a stated proportion of all values above it.
6. be able to assess normality

Analyzing patterns in scatterplots
* Correlation and linearity
* Median-median line
* Residual plots
* Least Squares line
* Outliers and influential points
* Re-expression of data
* Fitting models to data

1. Identify explanatory and response variables.
2. Make a scatterplot, and be able to include a categorical variable.
3. Describe the form, direction, and strength of the overall pattern of a scatterplot, as well as outliers and potentially influential observations.
4. Find and know the basic properties of correlation.
5. Explain slope and intercept from a linear regression equation.
6. Find the least-squares regression line with a calculator.
7. Use a regression line for prediction. Recognize extrapolation and be aware of its dangers.
8. Use r^2 to describe how much of the variation in one variable can be accounted for by a straight-line relationship with another variable.
9. Calculate and plot residuals and recognize unusual patterns.

* Modeling nonlinear relationships
* interpreting correlation and regression
* Relations in categorical data

1. recognize that exponential growth (or decay) results when a variable is multiplied by a fixed number greater than 1 (or positive number less than 1) in each time period.
2. recognize that a power function is the result of one variable being proportional to a power of a second variable.
3. Use semi-log transformations to linearize exponential data; use log-log transformations to linearize power relationships. Use least-squares regression on the transformed points, and inverse transformations to produce a curvilinear model for the original points.
4. Plotting residuals for the transformed data against a fitted line makes it easier to determine deviations from the overall pattern.
5. understand that both r and the least-squares regression line can be strongly influenced by a few extreme observations.
6. recognize possible lurking variables that may explain the observed association betgween two variables.
7. understand that even a strong correlation does not mean tghat there is a cause-and-effect relationship between x and y.
8. from a two-way table of counts, find the marginal distributions of both variables.
9. express any distribution in percents by dividing the category counts by their total.
10. describe the relationships between two categorical varibles by computing and comparing percents, usually by comparing the conditional distributions of one variable for the different categories of the other variable.

graded

* Methods of data collection -- census, sample survey, experiment, observational study
* Planning and conducting surveys
* Simple random sampling
* Stratifying to reduce variation
* Questionnaire design

* Planning and conducting experiments
* Randomized comparative experiments
* Blocking to reduce variation

1. identify the population in a sampling situation.
2. recognize bias due to voluntary response samples and other inferior sampling methods.
3. use a table of random digits or a calculator to select a simple random sample (SRS) from a population.
4. recognize the presence of undercoverage and nonresponse as sources of error in a sample survey. recognize the effect of the wording of questions on the response.
5. Use random digits to select a stratified random sample from a population when the strata are identified.
6. recognize whether a study is an observational study or an experiment.
7. recognize bias due to confounding of explanatory variables with lurking variables in either a study or an experiment.
8. Identify the factors, treatments, response variables, and experimental units or sub jects in an experiment.
9. outline the design of a completely randomized experiment using a diagram to include the size of the groups, the specific treatments, and the response varible.
10. Use a table of random digits to carry out the random assignment of subjects to groups in a completley randomized experiment.
11. recognize the placebo effect. recognize when double-blind techniques should be used.
12. Explain why a randomized comparative experiment can give good evidence for cause-and-effect relationships.
13. Recognize that many random phenomena can be investiat4ed by means of a carefully designed simulation.
14. Run a simulation by a) stating the problem or describe the experiment b)stating the assumptions c) assign digits to represent outcomes d) simulate many repetitions e) calculate relative frequencies and state your conclusions
15. Use a random number table, a calculator, or software to conduct simulations.

Multiplication, addition, and complement principles
* Probability of events occurring together
* Conditional probability
* Independent and mutually exclusive events

1. Describe the sample space of a random phenomenon. For a finite number of outcomes, use the multiplication principle to determine the number of outcomes, and use counting techniques, Venn diagrams, and tree diagrams to determine simple probabilities. For the continuous case, use geometric areas to find probabilities (areas under simple density curves) of events (intervals on the horizontal axis).
2. Know the probability rules and be able to apply them to determine probabilities of defined events. In particular, determine if a given assignment of probabilities is valid.
3. Determine if two events are disjoint, complementary, or independent. Find unions and intersections of two or more events.
4. Know the general addition rule for the union of two events, and define joint probability. Apply these characterizations to solve problems.
5. Define conditional probability and use the definition to find conditional probabilities of events.
6. Use the multiplication rule to find the joint probability of two events.
7. construct tree diagrams to organize the use of the multiplication and addition rules to solve problems with several states.

discrete and continuous random variables;
means and vafriances of random variables

1. Recognize and define a discrete random variable, and construct a probability distribution table and a probability histogram for the random variable.
2. Recognize and define a continuous random variable, and determine probabilities of events as areas under density curves.
3. Given a normal random variable, use a table or calculator to find probabilitis of events as areas under the stand normal distribution curve.
4. Calculate the man and variance of a discrete rnadom variable. Find th expected payout in a raffle or similar game of chance.
5. use simulation methods and the law of large numbers to approximate the mean of a distribution.
6. Use rules for mans and rules for variances to solve problems involving sums and differences of random variables.

Binomial Distributions; Binomial Probabilities; Binomial Formulas; Simulating Binomial Experiments; Mean and Standard Deviation of a Binomial Random Variable;
Geometric Distributions; Geometric Probabilities; Mean of a Geometric Random Variable

1. Identify a rnadom variable as binomial by verifying four conditions.
2. Use the calculator or the formula to determine binomial probabilities and construct probability distributions tables and histograms.
3. Calculate cumulative distribution functions for binomial random variables and construct cumulative distribution tables and histograms.
4. Calculate means (expected values) and stand deviations of binomial random variables.
5. Identify a random variable as geoemtric by verifying four consitions.
6. use formulas or a calculator to determine geometric probabilities and construct probability distribution tables and histograms.
7. Calculate cumulative distribution functions for geometric random varibles and construct cumulative distribution tables and histograms.
8. Calculate expected values of geometric random variables.

Sampling Distributions; Parameter vs. Statistic; Bais and Variability; Sample proportions; Standard deviation of sample proportions can be found when the population is at least 10 times the sample size; The normal approximation to the sampling distribution of sample proportions can be used if np>=10 and n(!1-p)>=10; Sample Means; Sample Means from a Normal Population; Central Limit Theorem; Law of Large Numbers

1. identify parameters and statistics in a sample or experiment.
2. Recognize the fact of sampling variability: a statistic will take different values when you repeat a sample or experiment.
3. Interpret a sampling distribution as describing the values taken by a statistic in all possible repetitions of a sample or experiment under the same condition.
4. Describe the bias and variability of a statistic int erms of the man and spread of its sampling distribution.
5. Understand that the variability of a statistic is controlled by the size of the sample (larger samples are less variable).
6. Recognize when a problem involves a sample proportion, p-hat.
7. Find the mean and standard deviation of a sample proportion for an SRS of size n from a population having population proportion pi.
8. Know that the standard deviation of the sampling distribution of p-hat gets smaller at the rate of the square root of n, as n gets larger.
9. Recognize when you can use the normal approximation to the sampling distribution of p-hat. Use the normal approximation to calculate probabilities that concern p-hat.
10. Recognize when a problem involves the mean x-bar of a sample.
11. Find the mean and standard deviation of a sample mean x-bar from an SRS of size n when the man mu and standard deviation sigma of the population are known.
12. Know that the standard deviation of teh sampling distribution of x-bar gets smaller at the rate of the square root of n as the sample size n gets larger.
13. understand that x-bar has approximately a normal distribution when the sample is large (central limit theorem). Use this normal distribution to calculate probabilities that concern x-bar.
14. use the law of large numbers to interpet the population mean mu as the average of an indefinitely large number of observations drawn from the population.

Logic of confidence intervals, significance testing, null and alternative hypotheses; p-values, one and two-sided tests; Type I and Type II errors; power

1. State in nontechnical language what is meant by "95% confidence." Interpret confidence level as well as the interval.
2. Calculate a confidence interval for the mean mu of a normal population with known standard deviation sigma.
3. Recognize when you can safely use the confidence interval formaula and when the sample design or a small sample from a skewed population makes it inaccurate.
4. Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.
5. Find the sample size required to obtain a confidence interval of specified margin of error m when the confidence level and other information are given.
6. Determine what Type I and Type II errors are in the context of a situation. Recognize that for a significance level alpha, alpha is the probaiblity of a Type I error, and the power against a specific alternative is 1 minutes the probability of a Type II error for that alternative.
7. Recognize that increasing the size of the sample increases the pwoer (reduces the probability of Type II error) when the significance level remains fixed.
8. State the null and alternative hypotheses in a testing situation when the parameter in question is a poulation mean mu.
9. Explain in nontechnical language the meaning of the P-value when you are given th4e numerical value of p for a test.
10. Calculate the z statistic and the P-value for both one-sided and two-sided tests about the mean mu of a normal population.
11. Assess statistical significance at standard levels alpha, either by comparing p to alpha or by comparing z to standard normal critical values.
12. Recognize that significance testing does not measure the siZe or importance of an effect.
13. Recognize when you can use the z test and when the data collection design or a small sample from a skewed population makes in appropriate.

t-distributions; t-confidence intervals and tests; matched pairs t-procedures; assumptions for inference about a proportion; z procedures; choosing sample size

1. Recognize when a problem requires inference about a mean or a proportion.
2. Recognize from the design of a study whether one-sample, matched pairs, or a single proportion procedure is needed.
3. use the t-procedures to obtain a confidence interval at a stated level of confidence for the mean mu of a popultion.
4. Carry out a t-test for the hypothesis that a population mean mu has a specified value against either a sone-sided or a two-sided alternative.
5. recognize when the t-procedures are appropriate in practice, in particulat that they are quite robust against lack of normality but are influenced by outliers.
6. Also recognize when th4e design of th4e study, outliers, or a small sample from a skewed distribution make the t-procedures risky.
7. Recognize matched pairs data and use the t-procedures to obtain confidence intervals and to perform tests of significance for such data.
8. Calculate from sample counts the sample proportion that estimates the population proportion.
9. Use the z procedure to give a confidence interval for a population proportion pi.
10. Use the z statistic to carry out a test of significance for the hypothse about a population proportion pi against either a one-sided or a two-sided alternative.
11. Check that you can safely use z procedures in a particular setting.

comparing two means; two-sample t-procedures; robustness; technology for more accurate levels in the t-procedures; pooled two-sample t-procedures; the sampling distribution of p-hat 1 minus p-hat 2; confidence intervals for pi 1 minus pi 2; significance tests for pi 1 minus pi 2.

1. Give a confidence interval for the difference between two means. Use the two-sample t statistic with conservative degrees of freedom or the calculator.
2. Test the hypothesis that two populations have equal means against either a one-sided or two-sided alternative. use the two-sample t test with conservative degrees of freedom or [preferably] a calculator or software.
3 Recognize when the two-sample t procedures are appropriate in practice.
4. use the two-sample z procedure to give a confidence interval for the difference pi 1 - pi 2 between proportions in two populations based on independent samples from the population.
5. use a z statistic to test the hypothese that proportions in two distinct populations are equal.
6. check that you can safely use 2-proportion z procedures in a particular setting.

test for goodness of fit; chi-square distributions; expected counts; inference for two-way tables: independent SRS's from each of several populations with each individual classified acccording to one categorical variable (the other variable says which sample the individual comes from); a single SRS with each individual classified according to both of two categorical variables; an entire poulation, with each individual classified according to both of two categorical variables

1. For goodness of fit, calculate expected counts for each category in a distribution, the chi-squared statistic, and the p-value.
2. State null and alternative hypotheses for a difference between two distributions.
3. If the test is significant, use components of the chi-square statistic to identify the most important deviations between observed and expected counts.
4. Arrange data on successes and failures in several groups into a two-way table of counts of successes and failures in all groups.
5. Use percents to describe the relationships between two categorical variables starting from the counts in a two-way table.
6. Locate expected cell counts, the chi-square statistic, and its P-value in output from software or calculator.
7. Explain what null hypothesis the chi-square statistic tests in a specific two-way table.
8. If a test of independence is significant, use percents, comparison of expected and observed counts, and the components of the chi-square statistic to see what deviations from the null hypothesis are most important.
9. In doing the chi-square test, calculate the expected count for any cell from the observed counts in a two-way table.
10. Calculate the component of the chi-square statistic for any cell, as well as the overall statistic.
11. Give the degrees of freedom of a chi-square statistic.
12. Use the chi-square critical values from a table to approximate the P-value of a chi-square test.

Assumptions for inference: SINR [S: Standard deviation of responses about the true line is the same for each x; I: Independent observations; N: Normal distribution of responses about the line [check residuals for normality!]; R: Randomly selected observations]; standard error s about the line; confidence interval for regression slope; testing the hypothesis of no linear relationship [test for regression slope]

1. Make a scatterplot to show the relationship between an explanatory and a response variable.
2. use a calculator or software to find the correlation and the least-squares regression line.
3. Inspect the data to recognize situations in which inference isn't safe: a nonlinear relationship, influential observations, strongly skewed residuals in a small sample, or nonconstant variation of the data points about the regression line].
4. Explain in any specific regression setting th4e meaning of th4e slope beta of the true regression line.
5. Understand computer output for regression. find in the output the slope and intercept of the least-squares line, their standard errors, and the standard error about the line.
6. Use that information to carry out tests and calculate confidence intervals for beta.

Review of all units

1. Familiarization with the format of the AP exam.
2. Strategies for answering (or leaving blank) multiple choice questions.
3. Strategies for answering the free response, especially the investigative task.
4. Time management for completion of the exam.
5. Effective use of the calculator for statistical computations, simulations, and graphical displays.