Ridgefield Public Schools

AP Statistics - High School

COURSE OBJECTIVE:

The purpose of this course is to introduce the major concepts and tools for collecting, analyzing and drawing conclusions from data. The course covers four broad concept areas: exploring data, planning a study, anticipating patterns – probability and statistical inference.

Throughout the year the students will complete in depth analyses of statistical problems. Students will use appropriate vocabulary to explain how data is collected, how test results are calculated, and interpret and communicate the results in context of the study. This vertical integration of knowledge allows the student to incorporate all aspects of the statistical process from design, through analysis, to conclusion. In addition to the aptitude for running a comprehensive statistical analysis of their own, the students will be qualified to critique other statistical studies for accuracy and significance of results.

Organizing Data: Looking for Patterns and Departure from Patterns (early September)

TOPICS

Exploring Data
The Normal Distribution
Examining Relationships
Two-Variable Data

CONTENT

INITIAL UNDERSTANDING

Display one variable data using a variety of display methods including: Dotplot, Histogram, Stemplot, Time Plot, and Boxplot.
Using the statistical features of the ti graphing calculator, the student will be able to calculate the measures of central tendency: Mean, Median, and Mode
Calculate measures of spread: Range, Five Point Summary, Interquartile range, and Standard Deviation.
Calculate the proportion of values above or below a stated number, or between two stated numbers, given that the variable is normally distributed with a stated mean and standard deviation.
Using statistical vocabulary, describe the overall shape of the distribution of data.
Determine if the data is quantitative or categorical.
Using the statistical features of the ti graphing calculator, the student will be able to display a scatterplot for two quantitative variables.
Using the statistical features of the ti graphing calculator, the student will be able to calculate the correlation coefficient, r, for small sets of observations using a calculator
Using the statistical features of the ti graphing calculator, the student will be able to calculate the leastsquares regression line of a response variable on an explanatory variable using a calculator.

DEVELOPING AN INTERPRETATION

Using statistical vocabulary, interpret normal probability plots.
Use the 689599.7 rule and symmetry to state what percent of the observations from a normal distribution fall between two points when both points lie at the mean or one, two, or three standard deviations on either side of the mean.
Recognize strong trends and other patterns in a time plot.
Determine if any outliers exist in a data set.
Determine if a distribution is bell shaped.
Identify the explanatory and response variables in situations where one variable explains or influences the other.
Using the statistical features of the TI graphing calculator, the student will be able to calculate and then plot residuals against the explanatory variable.
Recognize positive or negative association, a linear pattern, and outliers in a scatterplot.
Recognize relations in categorical data by calculating percentages.
Using the statistical features of the ti graphing calculator, the student will be able to create regression models nonlinear data.

MAKING CONNECTIONS

Predict values for a response variable given values of an explanatory variable, while recognizing the risk in using extrapolation.
Use residual plot to determine the viability of the least squares regression model.
Recognize how lurking variables may explain observed associations between two variables.
Using statistical vocabulary, describe how much of the variation in one variable can be accounted for by a straightline relationship with another variable, by using the coefficient of determination.

TAKING A CRITICAL STANCE

Defend a survey’s use of the normal probability distribution by comparing observations with the 689599.7 rule for normal distribution
Using statistical vocabulary, evaluate the validity of the cause and effect relationships described in research case studies with special attention to the pitfalls of lurking variables, and influential observations, and communicate the findings of the evaluation.
Using statistical vocabulary, support the researcher’s choice for a measure of center and spread as the descriptor of the data set.

Producing Data: Samples and Experiments (early November)

CONTENT

INITIAL UNDERSTANDING

Identify the population in a sampling survey
Using statistical vocabulary, describe the difference between a survey and an experiment.
Understand what a simple random sample is.
Use a table of random digits to assign probabilities of outcomes.
List the principles of experimental design

DEVELOPING AN INTERPRETATION

Recognize pitfalls of survey design including bias, under coverage, and non response.
Recognize the pitfalls in experimental design including, bias and confounding.
Paraphrase the statement “Association does not mean causation” in your own words.
Using statistical vocabulary, discuss when it is best to conduct a survey, when it is best to conduct an experiment, and when it is best to simulate.
Using statistical vocabulary, defend the need for randomization in both surveys and experiments.
Using statistical vocabulary, explain the need for a control group in the design of an experiment.

MAKING CONNECTIONS

Using statistical vocabulary, compare and contrast stratified random sampling of a survey with block design of an experiment
Design a simulation of an experiment using a table of random digits, in order to duplicate the results of an experiment of known probabilities.
Display the results of a survey or an experiment using the techniques learned under data presentation.

TAKING A CRITICAL STANCE

Using statistical vocabulary, defend or dispute the result of a study by simulating the experiment and comparing the results of the simulation with the results of the study.

Probability: Foundations of Inference (early December)

TOPICS

Probability: The Study of Randomness
Random Variables
The Binomial and Geometric Distributions
Sampling Distributions

CONTENT

INITIAL UNDERSTANDING

Using statistical vocabulary, define a random phenomenon
Using statistical vocabulary, define probability of an event
Identify complementary events
Identify a random variable.
Using statistical vocabulary, explain the difference between a discrete random variable and a continuous random variable.
Using statistical vocabulary, define density curve.
Using statistical vocabulary, paraphrase the Law of Large Numbers.
Using statistical vocabulary, describe the characteristics necessary for the binomial setting.
Using statistical vocabulary, describe the characteristics necessary for the geometric setting
Using statistical vocabulary, explain the difference between a binomial distribution, and a geometric distribution.
Using statistical vocabulary, explain the difference between a parameter and a statistic.
Identify bias and variability in a statistic.
Using statistical vocabulary, explain the difference between a sample proportion and a sample mean.
Paraphrase the Central Limit Theorem.

DEVELOPING AN INTERPRETATION

Construct a tree diagram to display the sample space of a random phenomenon.
Construct a Venn diagram to display the sample space of a random phenomenon.
Apply addition rules of probability for events that are joint or disjoint.
Apply multiplication rule of probability for independent or conditional events.
Construct a probability histogram of a discrete random variable.
Using the statistical features of the TI graphing calculator, the student will be able to calculate the probabilities of a continuous random variable with uniform distribution
Using the statistical features of the TI graphing calculator, the student will be able to calculate the mean and standard deviation of a discrete random variable.
Apply the rules for the sums of means and variances of random variables.
Using the statistical features of the TI graphing calculator, the student will be able to calculate the probabilities associated with a binomial distribution
Using the statistical features of the TI graphing calculator, the student will be able to calculate the mean and standard deviation of a binomial random variable.
Using the statistical features of the TI graphing calculator, the student will be able to calculate the probabilities associated with a geometric distribution.
Using the statistical features of the TI graphing calculator, the student will be able to calculate the mean or expected value of a geometric random variable.
Determine if an item of interest is a parameter or a statistic
Describe how bias and variability of a statistic can be limited by randomization and sample size.
Using the statistical features of the TI graphing calculator, the student will be able to calculate the mean and standard deviation of a sample proportion
Using the statistical features of the TI graphing calculator, the student will be able to calculate the mean and standard deviation of a sample mean.

MAKING CONNECTIONS

Use geometric area formulas to determine areas under simple density curves to find probabilities of events.
Compare theoretical binomial probabilities calculated by formula with binomial probabilities derived though methods of simulation.
Describe a sampling distribution using terminology from previous units, including a description of shape, and measures of center and spread.
Confirm the Central Limit Theorem through the use of simulation or experimentation.

TAKING A CRITICAL STANCE

Determine if a given assignment of probabilities used in a study is valid. Use methods of simulation, calculation of areas, or other research techniques to support your conclusions.
Support the use of the binomial setting in a research paper. Be sure to evaluate the conditions that allow the author to apply the laws governing the binomial setting.
Evaluate a study with respect to undue sources of bias or variance. Confirm that measures have been taken to successfully eradicate these issues as a source of error.

Inference: Conclusions with Confidence (mid February)

TOPICS

Introduction to Inference
Inference for Distributions
Inference for Proportions
Inference for Tables: ChiSquare Procedures
Inference for Regression

CONTENT

INITIAL UNDERSTANDING

Using statistical vocabulary, define z^*.
Using statistical vocabulary, explain how the margin of error is influenced by z^*, σ, and n.
State the null hypothesis and alternative hypothesis in a test of significance.
Using statistical vocabulary, define a Pvalue.
Using statistical vocabulary, define α, the significance level.
Using statistical vocabulary, define the z test statistic.
Using statistical vocabulary, describe the difference between type I and type II errors.
List the assumptions necessary in order to make inferences about the mean in a t procedure.
Using statistical vocabulary, explain when a confidence interval or significance test is called robust.
List the assumptions necessary for comparing two means in a t procedure.
State the assumptions necessary for inference about a proportion.
Describe the circumstances when it is best to use a Chisquare test for goodness of fit.
Using statistical vocabulary, explain the distinction between confidence intervals
for the mean response and a prediction interval for the individual response.

DEVELOPING AN INTERPRETATION

Using the statistical features of the ti graphing calculator, the student will be able to calculate a confidence interval for a population mean
Using the statistical features of the ti graphing calculator, the student will be able to calculate a margin of error about a mean of a population.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a sample size given a margin of error in a z procedure.
Using the statistical features of the ti graphing calculator, the student will be able to calculate the probability of a type I error
Using the statistical features of the ti graphing calculator, the student will be able to calculate the power of a test against its alternative
Using the statistical features of the ti graphing calculator, the student will be able to calculate a t value for a set of data
Using the statistical features of the ti graphing calculator, the student will be able to calculate a confidence interval around the mean of a sample.
Conduct a test of significance about the mean of a sample.
Illustrate the use of a matched pairs t procedure.
Recognize when a problem requires inference about a mean or comparing two means.
Recognize, from the design of a study, whether one sample, matched pairs or two sample procedures are needed.
Using the statistical features of the ti graphing calculator, the student will be able to calculate the t value when comparing two means.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a confidence interval about the difference of two means.
Conduct a test of significance when comparing two means.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a z value for a proportion.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a confidence interval about the mean of a proportion.
Conduct a test of significance around a proportion.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a sample size for a margin of error in a proportion situation.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a z value for the difference of two proportions.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a confidence interval about the difference of two proportions.
Conduct a test of significance when comparing two proportions.
Using the statistical features of the ti graphing calculator, the student will be able to calculate a Chisquare value for a goodness of fit test or a test of association.
Conduct a Chi square test for goodness of fit.
Using the statistical features of the ti graphing calculator, the student will be able to calculate the standard error about the least squares line.
Conduct a test of significance for a regression slope.

MAKING CONNECTIONS

Examine the relationship between the chosen level of significance, and the situations under study. Why do some tests require a 95% level of confidence, while others require a 99% level of confidence?
Decide whether or not the use of a z test is appropriate based on the design of the data collection method, or the distribution of the data.
Decide whether or not the use of a t test, onesample or twosample, is appropriate based on the design of the study, or the distribution of data.
Decide whether or not the use of a Chisquare test is appropriate based on the design of the study, and the distribution of data.
Conduct a test of significance and give evidence for rejecting or failing to reject a hypothesis based on the test statistic. Student will begin by analyzing how data was collected and why data was collected. Student will decide on appropriate hypothesis and alternate hypothesis. After calculating test statistics and p value, student will interpret and explain the results of the test in context of the original problem.

TAKING A CRITICAL STANCE

Evaluate the use and results of a t test in a study. Confirm that the author has examined the criteria necessary in order to utilize this test, and has correctly analyzed the results of the test in drawing their conclusions.
Critique the use and results of a study using a z test in a proportion. Confirm that the author has examined the criteria necessary in order to utilize this test, and has correctly analyzed the results of the test in drawing their conclusions.
Critique a study that used a linear relationship to make a prediction by carrying out tests of significance for slope of the line. Look for situations in which the inference is not safe: primarily, nonlinear relationships, skewed residuals in a small sample, or nonconstant variation of the data about the regression line.

AP Exam Review and AP Exam (early April)

The AP Statistics Exam is given in May.

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