Syllabus

Primary Textbook

Bock, David E., Paul F. Velleman, and Richard D. DeVeaux. Stats: Modeling the World. 3rd Edition. Boston: Pearson/Addison-Wesley, 2007

Bock, David E., Paul F. Velleman, and Richard D. DeVeaux. Stats: Modeling the World. 2nd Edition. Boston: Pearson/Addison-Wesley, 2004

 

Resource Materials

Bock, David E., William B. Craine III. Stats: Modeling the World: Printed Test Bank and Resource Guide. Boston: Pearson/Addison-Wesley, 2007.

Humphrey, Patricia, David E. Bock, William B. Craine III. Stats: Modeling the World: TI-83/84 Plus and TI-89 Manual. Boston: Pearson/Addison-Wesley, 2004.

Bohan, James F. AP Statistics: Preparing for the Advanced Placement Examination. New York: Amsco School Publications, Inc., 2006

 

Technology

TI-83 Plus or better Graphing Calculators; Minitab 14 software; Autograph software; ActivStats software

 

Miscellaneous Materials

Handouts of correctly solved even numbered problems from each chapter from the text; formula sheets from AP Central; Past AP questions from AP Central 3

 

AP Statistics Course Outline

The 4 conceptual themes are woven throughout the course. The following Chapters are broken up into quarters. (Note: There are approximately 45 days per quarter – any “left over days” not accounted for in “Class Days” are for review, assessment purposes, assemblies, snow days etc.) I have listed most of the skills learned with each Chapter (as quoted from the text book) along with chapter exercises, graphing calculator explorations, quizzes, ActivStats, Investigative tasks, and tests. I have taught this course for 2 years and both years I failed to spend as much time as needed on the information in the last few chapters – it is my hope that if I follow closely the course outline suggested by Boch, I will far surpass the needed material and hold the students to a high standard of learning, as an AP class should be. It is because of this that I have set up the course outline according to the text chapters.

 

Quarter 1:

Chapter 1 “Stats Starts Here” (Class Days: 1)

Skills:

 Describes text set-up

 

Chapter 2 “Data” (Class Days: 2)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Skills:

 Be able to identify and describe the who, what, when, where, why and how of data, or recognize when some of this information has not been provided

 Be able to identify the cases and variables in any data set

 Be able to classify a variable as categorical or quantitative depending on its use.

 For any quantitative variable be able to identify the units in which the variable has been measured (or note that they have not been provided)

Exercises: See Chapter 2 Exercises to be completed

Chapter 2 Quiz

Technology: Entering data into graphing calculator/computer software; ActivStats lesson1&2:types of data and context 4

 

Chapter 3 “Displaying and Describing Categorical Data” (Class Days: 3)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Skills:

 Be able to recognize when a variable is categorical and choose an appropriate display for it.

 Understand how to examine the association between categorical variables by comparing conditional and marginal percentages.

 Be able to summarize the distribution of a categorical variable with a frequency table.

 Be able to display the distribution of a categorical variable with a bar chart or pie chart.

 Know how to make and examine a contingency table.

 Know how to make and examine displays of the conditional distributions of one variable for two or more groups.

 Be able to describe the distribution of a categorical variable in terms of its possible values and relative frequencies.

 Know how to describe and discuss any anomalies or extraordinary features revealed by the display of a variable.

 Be able to describe and discuss patterns found in a contingency table and associated displays of conditional distributions.

Exercises: See Chapter 3 Exercises to be completed

Chapter 3 Quiz

Technology: Using software to display data; ActivStats lesson 3-1: distribution on 1 variable, displays of categorical data 5

 

Chapter 4 “Displaying Quantitative Data” (Class Days: 4)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Skills:

 Be able to identify an appropriate display for any quantitative variable.

 Be able to guess the shape of the distribution of a variable by knowing something about the data.

 Know how to display the distribution of a quantitative variable with a stem-and-leaf display, a dot plot, and/or a histogram (by hand, graphing calculator, software)

 Know how to make and describe a time plot of data that may vary over time

 Be able to describe the distribution of a quantitative variable in terms of its shape, center, and spread.

 Know how to describe any anomalies or extraordinary features revealed by the display of a variable.

 Know how to compare the distributions of two or more groups by comparing their shapes, centers, and spreads.

 Be able to discuss any outliers in the data, noting how they deviate from the overall pattern of the data.

Exercises: See Chapter 4 Exercises to be completed

Chapter 4 Quiz

Technology: TI-83/software – how to make histograms and dotplots( ActivStats)

Investigative Task: Dollars for Students 6

 

Chapter 5 “Displaying Distributions Numerically” (Class Days: 5)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Skills:

 Be able to select a suitable measure of center and a suitable measure of spread for a variable based on information about its distribution.

 Know the basic properties of the median: The median divides the data into halves.

 Know the basic properties of the mean: The mean is the point at which the histogram balances.

 Know that the standard deviation summarizes how spread out all the data are around the mean.

 Know how to compute the mean, median, standard deviation, 5 number summary, IQR of a set of data.

 Be able to construct a boxplot (by hand, by calculator, and by software).

 Understand that the median and IQR resist the effects of outliers, while the mean and standard deviation do not.

 Understand that in a skewed distribution, the mean is pulled in the direction of the skewness relative to the median.

 Know how to describe summary measures in a sentence.

 Be able to describe the distribution of a quantitative variable with a description of the shape of the distribution, a numerical measure of center, and a numerical measure of spread. Noting any unusual features (outliers).

Exercises: See Chapter 5 Exercises to be completed

Chapter 5 Quiz

Technology: Boxplots, 1 variable statistics on TI83/software; ActivStats: standard deviation

Investigative Task: Auto Safety 7

 

Chapter 6 “The Standard Deviation as a Ruler and the Normal Model” (Class Days: 7)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

Skills:

 Understand how adding (subtracting) a constant or multiplying (dividing) by a constant changes the center and/or spread of a variable.

 Recognize when standardization can be used to compare values.

 Understand that standardizing uses the standard deviation as a ruler.

 Recognize when a Normal model is appropriate.

 Know how to calculate the z-score.

 Know how to compare values of two different variables using their z-scores.

 Be able to use Normal models and the Empirical Rule to estimate the percentage of observations falling 1, 2 or 3 standardizations of the mean.

 Know how to find the percentage of observations falling below any value in a Normal model using a Normal table and appropriate technology.

 Know how to check whether a variable satisfies the Nearly Normal Condition by making a Normal probability plot or histogram.

 Know what a z-score is and be able to explain how extraordinary (or not) a value may be by using a Normal model.

Exercises: See Chapter 6 Exercises to be completed

Chapter 6 Quiz

Technology: Using normalpdf; normalcdf; invnorm on TI83; scatterplots on TI83/software; ActivStats lesson 6: Normal model

TEST: UNIT 1 (chapters 1-6) 8

 

Chapter 7 “Scatterplots, Association, and Correlation” (Class Days: 3)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Recognize when interest in the pattern of possible relationship between two quantitative variables suggests making a scattterplot.

 Know how to identify the roles of the variables and to place the response variable on the y-axis and the explanatory variable on the x-axis.

 Know the conditions for correlation and how to check them.

 Know that correlations are between -1 and 1, and that each extreme indicates a perfect linear association.

 Understand how the magnitude of the correlation reflects the strength of a linear association as view in a scatterplot.

 Know that correlation has no units.

 Know that the correlation coefficient is not changed by changing the center or scale of either variable.

 Understand that causation cannot be determined by a scatterplot or correlation.

 Know how to make a scatterplot (by hand or appropriate technology).

 Know how to compute the correlation of two variables.

 Know how to read a correlation table produced by a statistics program.

 Be able to describe the direction, form, and strength of a scatterplot.

 Be able to describe points that deviate from the overall pattern.

 Be able to use correlation as part of the description of a scatterplot.

 Be alert to misinterpretations of correlation.

 Understand that finding a correlation between two variables does not indicate a causal relationship between them. Beware of the dangers of suggesting causal relationships when describing correlations.

Exercises: See Chapter 7 Exercises to be completed

Chapter 7 Quiz

Technology: Scatterplots, linear regression on TI83/software; ActivStats lesson 7:scatterplots 9

 

Chapter 8 “Linear Regression” (Class Days: 8)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Be able to identify response (y) and explanatory(x) variables in context.

 Understand how a linear equation summarizes the relationship between two variables

 Recognize when a regression should be used to summarize a linear relationship between two quantitative variables.

 Be able to judge whether the slope of a regression line makes sense.

 Know how to examine data for violations of the Straight Enough Condition that would make it inappropriate to compute a regression.

 Understand that the least squares slope is easily affected by extreme values.

 Know that residuals are the differences between the data values and the corresponding values predicted by the line and that the least squares criterion finds the line that minimizes the sum of the squared residuals.

 Know how to use a plot of the residuals against predicted values to check the Straight Enough Condition or look for outliers.

 Know how to find a regression equation from the summary statistics for each variable and the correlation between the variables.

 Know how to find the regression equation using statistics software and how to find the slope and intercept values in a regression output table.

 Know how to use regression to predict a value of y for a given x.

 Know how to compute the residual for each data value and how to display them.

 Be able to write a sentence explaining what a linear equation says about the relationship between y and x, basing it on the fact that the slope is given in y-units per x unit.

 Understand how the correlation coefficient and the regression slope are related.

 Be able to describe a prediction made from a regression equation, relating the predicted value to the specified x value.

Exercises: See Chapter 8 Exercises to be completed

Chapter 8 Quiz

Technology: residuals on TI83/software; ActivStats lesson 8: Least squares regression

Investigative Task: Smoking 10

 

Chapter 9 “Regression Wisdom” (Class Days:4)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Understand when to use a linear model.

 Look for subgroups in data before you find a regression, and analyze them separately.

 Know the danger of exploiting beyond the range of the x-values used to find the linear model, especially when the extrapolation tries to predict into the future.

 Understand the points may be unusual by having a large residual or by having high leverage.

 Understand that an influential point can change the slope and intercept of a regression line.

 Look for lurking variables whenever considering the association between two variables.

 Know how to display residuals from a linear model by making a scatterplot of the residuals against predicted values or against the x- variable, and know what patterns to look in the picture.

 Know how to examine a scatterplot.

 Include diagnostic information such as plots of residuals and leverages as part of your report of a regression.

 Report any high leverage points. Analyze data with and without any outliers.

 Include appropriate cautions about extrapolation when reporting predictions from a linear model.

 Discuss any lurking variables.

Exercises: See Chapter 9 Exercises to be completed

Chapter 9 Quiz

Technology: regression and residuals on TI83/software; ActivStats lesson 7: correlation tool; lesson 8 and 9: Linear regression

Investigative Task: Olympic Long Jump 11

 

Chapter 10 “Re-expressing Data” (Class Days: 8)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 

 Recognize when a well-chosen re-expression may be helpful.

 Understand the value of re-expressing data to improve symmetry, to make the scatter around a line more constant, or to make the scatterplot more linear.

 Recognize when the pattern of the data indicates that no re-expression can improve the structure of the data.

Know how to re-express the data with powers and how to find an effective re-expression for your data using statistics software or a calculator.

 Be able to reverse any of the common re-expressions to put a predicted value or residual back into the original data units.

 Be able to describe a summary or display of a re-expressed variable making clear how it was re-expressed and giving its re-expressed units.

 Be able to describe a regression model fit to re-expressed data in terms of the re-expressed variables.

Exercises: See Chapter 10 Exercises to be completed

Chapter 10 Quiz

Technology: re-expressing data on TI83/software; ActivStats lesson 10: re-expressing data

TEST: UNIT 2 (chapters 7-10) 12

 

Chapter 11 “Understanding Randomness” (Class Days: 4)

Conceptual Theme: Sampling and Experimentation: Planning and conducting a study

Curricular Requirements: The course provides instruction with appropriate emphasis on sampling and experimentation. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Skills

 Be able to recognize random outcomes in a real-world situation.

 Be able to recognize when a simulation might usefully model random behavior in the real world.

 Know how to perform a simulation either by generating random numbers on a computer, calculator, or by using some other source of random variables such as dice, a spinner, or a table of random numbers.

 Be able to describe a simulation so that others could repeat it.

 Be able to discuss the results of a simulation study and draw conclusions about the question being investigated.

Exercises: See Chapter 11 Exercises to be completed

Chapter 11 Quiz

Technology: Random number generator on the TI-83/software; ActivStats lesson 11: randomness

Investigative Task: ESP 13

 

Chapter 12 “Sample Surveys” (Class Days: 5)

Conceptual Theme: Sampling and Experimentation: Planning and conducting a study

Curricular Requirements: The course provides instruction with appropriate emphasis on sampling and experimentation. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Skills:

 Know the basic concepts of sampling.

 Recognize population parameters in descriptions of populations and samples.

 Understand the value of randomization as a defense against bias.

Understand the value of sampling to estimate population parameters from statistics calculated on representative samples drawn from the population.

 Understand that eh size of the sample determines the precision of estimates.

 Know how to draw a SRS from a master list of a population, using a computer or a table of random numbers.

 Know what to report about a sample as part of your account of a statistical analysis.

 Be able to report possible sources of bias in sampling methods.

 Recognize voluntary response and non-response as sources of bias in a sample survey.

Exercises: See Chapter 12 Exercises to be completed

Chapter `12 Quiz

Tehnology: ActivStats lesson 12: sample surveys 14

 

Chapter 13 “Experiments and Observational Studies” (Class Days: 6)

Conceptual Theme: Sampling and Experimentation: Planning and conducting a study

Curricular Requirements: The course provides instruction with appropriate emphasis on sampling and experimentation. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Skills:

 Recognize when an observational study is appropriate.

 Be able to identify observational studies as retrospective or prospective, and understand the strengths and weaknesses of each method.

 Know the four basic principles of sound experiment design: control, randomization, replication, and block, and be able to explain each.

 Be able to recognize the factors, the treatments, and the response variable in a description of a designed experiment.

 Understand the essential importance of randomization in assigning treatments to experimental units.

 Understand the importance of replication to move from anecdotes to general conclusions.

 Understanding the value of blocking so that variability due to differences in attributes of the subjects can be removed.

 Understand the importance of the control group and the need for a placebo treatment in some studies.

 Understand the importance of blinding and double blinding in studies on human subjects, and be able to identify blinding and the need for blinding in experiments.

 Understand the value of the placebo in experiments with human participants.

 Be able to design a completely randomized experiment to test the effect of a single factor.

 Be able to design an experiment in which blocking is used to reduce variation.

 Know how to use graphical displays to compare responses for different treatment groups.

 Know how to report the results of an observational study. Identify the subjects, how the data were gathered, and any potential biases or flaws you may be aware of. Identify the factors known and those that might have been revealed by the study.

 Know how to compare the responses in different treatment groups to assess whether the differences are larger than they could be reasonably expected from ordinary sampling variability.

 Know how to report the results of an experiment.

 Be able to report on the statistical significance of the result in terms of whether the observed group to group differences are larger than could be expected from ordinary sampling variation.

Exercises: See Chapter 13 Exercises to be completed

Chapter 13 Qui

Technology: ActivStats lesson 13: designed experiments

Investigative Task: Backhoe& Forklifts

TEST:UNIT III 15

 

Chapter 14 “From Randomness to Probability” (Class Days: 3)

Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation

Curricular Requirements: The course provides instruction with appropriate emphasis on anticipating patterns. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Understand that random phenomena are unpredictable in the short term but show long-run predictability.

 Be able to recognize random outcomes in a real-world situation.

Know that the relative frequency of an outcome of a random phenomenon settles down as we gather more random outcomes.

 Be able to state the Law of Large Numbers.

 Know the basic definitions and rules of probability.

 Recognize when events are disjoint and when events are independent. Understand the difference, and that disjoint events cannot be independent.

 Be able to use the facts abut probability to determine whether an assignment of probabilities is legitimate. Each probability must be between 0 and 1 and the sum of the probabilities assigned to all possible outcomes must be 1.

 Know how and when to apply the addition rule. Know that events must be disjoint for the addition rule to apply.

 Know how and when to apply the multiplication rule. Know that events must be independent for the multiplication (combinations).

 Complement rule ( at least).

 Be able to use statements about probability in describing random phenomenon.

 Know and correctly use vocabulary with respect to probability.

Exercises: See Chapter 14 Exercises to be completed

Chapter 14 Quiz

Investigative Task: Dollars for Students

Technology: use the TI-83/software for arithmetic; ActivStats lesson 14:LLN 16

 

Chapter 15 “Probability Rules” (Class Days: 4)

Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation

Curricular Requirements: The course provides instruction with appropriate emphasis on anticipating patterns. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Understand that the probability of an event is the proportion of times it occurs in many repetitions of a random phenomenon.

 Understand Conditional probability.

 Understand the concept of Independence.

 Know how and when to apply the General Addition/Multiplication Rules.

 Know how to find probabilities for compound events using a 2 way table.

 Know how to make and use a tree diagram.

 Be able to make a clear statement about a conditional probability that makes clear how the condition affects the probability.

 Avoid making statements that assume independence when there is none.

Exercises: See Chapter 15 Exercises to be completed

Chapter 15 Quiz

Technology: use the TI-83/software for arithmetic; ActivStats lesson 15: conditional probability and independence 17

 

Chapter 16 “Random Variables” (Class Days: 4)

Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation

Curricular Requirements: The course provides instruction with appropriate emphasis on anticipating patterns. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Be able recognize random variables.

 Understand that random variables must be independent in order to determine the variability of their sum or difference by adding variances.

 Be able to find the probability model for a discrete random variable.

 Know how to find the expected mean and variance of a random variable. (and adding and multiplying constants; adding or subtracting 2 independent random variables.)

 Stress proper notation.

 Be able to interpret the meaning of the expected value and standard deviation of a random variable in the proper context.

Exercises: See Chapter 16 Exercises to be completed

Chapter 16 Quiz

Technology: Finding the expected mean and standard deviations using lists and 1- variable stats on the TI-83/software. ActivStats lesson 16 randomness and CLT 18

 

Chapter 17 “Probability Models” (Class Days: 6)

Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation

Curricular Requirements: The course provides instruction with appropriate emphasis on anticipating patterns. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Know how to tell if a situation involves Bernoulli trials.

 Be able to choose whether to use a Geometric or a Binomial model for a random variable involving Bernoulli trials.

 Know and state the appropriate conditions for using a Geometric, Binomial, or Normal model.

 Know how to find the expected value of a Geometric model.

 Be able to calculate Geometric and Binomial probabilities.

 Know how to find the mean and standard deviation of a Binomial model.

 Be able to estimate with a Normal model.

 Be able to interpret means, standard deviations, and probabilities in the Bernoulli trial context.

Exercises: See Chapter 17 Exercises to be completed

Chapter 17 Quiz

Technology: finding Geometric and Binomial Probabilities on the TI-83/software ActivStats lesson 17: probability models

TEST:UNIT IV

Mid-term Project (Class Days:5) 19

 

Chapter 18 “Sampling Distribution Models” (Class Days:4)

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Understand that the variability of a statistic depends on the size of the sample.

 Understand the Central Limit Theorem.

 Be able to demonstrate a sampling distribution by simulation.

 Be able to use a sampling distribution model to make simple statements about the distribution of a proportion or mean under repeated sampling.

 Be able to interpret a sampling distribution model as describing the values taken by a statistic in all possible realizations of a sample or randomized experiment under the sample conditions.

Exercises: See Chapter 18 Exercises to be completed

Chapter 18 Quiz

Technology: use the TI-83/software to help compute standard error; ActivStats lesson 18 CLT

Investigative Task: Simulated Coins 20

 

Chapter 19 “Confidence Intervals for Proportions” (Class Days: 4)

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Understand confidence intervals as a balance between the precision and the certainty of a statement about a model parameter.

 Understand the margin of error of a confidence interval for a proportion changes with the sample size and the level of confidence.

 Know hoe to examine your data for violations of conditions that would make inference about a population proportion unwise or invalid.

 Be able to construct a one-proportion z-interval.

 Be able to interpret a one-proportion z-interval in a simple sentence or two.

Exercises: See Chapter 19 Exercises to be completed

Chapter 19 Quiz

Technology: creating a one-proportion z-interval on the TI-83/software; ActivStats lesson 19: inference for proportions 21

 

Chapter 20 “Testing Hypotheses about Proportions” (Class Days: 2)

Concptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Be able to state the null and alternative hypotheses for a one-proportion z-test.

 Know the conditions that must be true for a one-proportion z-test to be appropriate and know how to examine your data for violations of those conditions.

 Be able to identify and use the alternative hypothesis when testing hypotheses.

 Understand how to choose between a one-sided and a two-sided alternative hypothesis and be able to explain your choice.

 Be able to perform a one-proportion z-test.

 Be able to write a sentence interpreting the results of a one-proportion z-test.

 Know how to interpret a P-value both in general and in the context of a problem.

Exercises: See Chapter 20 Exercises to be completed

Chapter 20 Quiz

Technology: Do a one-proportion z-test on the TI-83/software; ActivStats lesson 20:testing hypotheses 22

 

Chapter 21 “More about Tests” (Class Days: 3)

Conceptual Theme: Statistical Inference: Estimating population parameters is and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Understand the close relationship between hypothesis tests and confidence intervals.

 Be able to identify and use the alternative hypothesis when testing hypotheses.

 Understand how to choose between a one-sided and a two-sided alternative hypothesis and be able to explain your choice

 Understand how the critical value for a test is related to the specified alpha level.

 Understand Type I and Type II errors.

 Understand that the power of a test gives the probability that it correctly rejects a false null hypothesis when a specified alternative is true.

 Understand the role sample size as it pertains to Type I and Type II errors and the power of a test

 Know how to complete a hypothesis test for a population proportion.

 Be able to interpret the meaning of a P-value both in general and in the context of a problem.

 Be able to state whether based on P- values to either reject a null hypothesis or failed to reject it.

Exercises: See Chapter 21 Exercises to be completed

Chapter 21 Quiz

Technology: Continue to use the on the TI-83/software to help create confidence intervals and hypothesis tests; ActivStats lesson 21:interactive demonstrations

Investigative Task: Life after High School 23

 

Chapter 22 “Comparing Two Proportions” (Class Days: 4)

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Be able to state the null and alternative hypotheses for testing the difference between two populations.

 Know how to examine your data for violations of conditions that would make inference about the difference between 2 population proportions unwise or invalid.

 Understand that the formula for the standard error of the difference between 2 independent sample proportions is based on the principle that when finding the sum or difference of 2 independent random variables, their variances add.

 Know how to find a confidence interval for the difference between 2 proportions.

 Be able to perform a significance test of the natural null hypothesis that 2 population proportions are equal.

 Know how to write a sentence describing what is said about the difference between 2 population proportions by a confidence interval.

 Know how to write a sentence interpreting the results of a significance test of the null hypothesis that 2 population proportions are equal.

 Be able to interpret the meaning of a P-value in non-technical terms, making clear that the probability claim is made about computed values and not about the population parameter of interest.

 Know that we do NOT “accept” a null hypothesis if we fail to reject it.

Exercises: See Chapter 22 Exercises to be completed

Chapter 22 Quiz

Technology: 2 proportion z test and 2 proportion z-interval on the TI-83/software; ActivStats lesson 22: inference for 2 proportions

TEST: UNIT V 24

 

Chapter 23 “Inferences about Means” (Class Days: 3)

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Know the assumptions required for t-based confidence intervals.

 Know how to examine your data for violations of conditions that would make inference about the population mean unwise or invalid.

 Understand that a confidence interval and a hypothesis test are essentially equivalent.

 Be able to compute and interpret a t-test for the population mean using a statistics package or working from summary statistics.

 Be able to compute and interpret a t- based confidence interval for the population mean using a statistics package or working from summary statistics for a sample.

 Be able to explain the meaning of a confidence interval for a population mean.

 Understand that a 95%confidence interval does not trap 95% of the sample values.

 Be able to interpret the result of a hypothesis about a population mean.

 Understand that the P-value of a test does not give the probability that the null hypothesis is correct.

Exercises: See Chapter 23 Exercises to be completed

Chapter 23 Quiz

Technology: testing hypothesis given the samples mean and standard deviation using the TI-83/software; ActivStats lesson 23: confidence intervals and p-values

Investigative Task: SAT Performance 25

 

Chapter 24“Comparing Means” (Class Days: 2)

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Be able to recognize situations in which we want to do inference on the difference between the means of 2 independent groups.

 Know how to examine your data for violations of conditions that would make inference about the difference between 2 population means unwise or invalid.

 Be able to recognize when a pooled – t procedure might be appropriate and be able to explain why you decided to use a two sample method anyway.

 Be able to perform a two-sample t-test using a statistics package or calculator (finding degrees of freedom)

 Be able to interpret a test of the null hypothesis that the means of 2 independent groups are equal

Exercises: See Chapter 24 Exercises to be completed

Chapter 24 Quiz

Technology: 2 sample t-test on the TI-83/software; ActivStats lesson 24:comparing 2 means

Investigative Task: SAT Performance Part 2 26

 

Chapter 25 “Paired Samples and Blocks” (Class Days: 4)

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Be able to recognize whether a design that compares 2 groups is paired or not.

 Be able to find a paired confidence interval.

 Be able to perform a paired t-test.

 Be able to interpret a paired t-test.

 Be able to interpret a paired t-interval.

Exercises: See Chapter 25 Exercises to be completed

Chapter 25 Quiz

Technology: test a hypothesis about the mean of paired differences; finding a t- interval on the TI-83/software; ActivStats lesson 25: paired samples

TEST: UNIT VI 27

 

Chapter 26 “Comparing Counts” (Class Days: 6)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course provides instruction with appropriate emphasis on anticipating patterns. The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Be able to recognize when a test of goodness of fit, a test of homogeneity, or a test of independence would be appropriate for a table of counts.

 Understand that the degrees of freedom for a chi-square test depend on the dimensions of the table and not the sample size.

 Understand that increasing the sample size increases the ability of chi-square procedures to reject the null hypothesis.

 Be able to display and interpret counts in a two-way table.

 Know how to use chi-square tables to perform chi-square tests.

 Know how to compute a chi-square test using TI83/software.

 Be able to examine the standardized residuals to explain the nature of the deviations from the null hypothesis.

 Know how to interpret chi-square as a test of goodness of fit in a few sentences.

 Know how to interpret chi-square as a test of homogeneity in a few sentences.

 Know how to interpret chi-square as a test of independence in a few sentences.

Exercises: See Chapter 26 Exercises to be completed

Chapter 26 Quiz

Technology: testing a hypothesis of homogeneity or independence; using matrices for chi-square testing with the TI-83/software; ActivStats lesson:26 chi-square

Investigative Task: ’97 AP STAT Scores 28

 

Chapter 27 “Inferences for Regression” (Class Days: 6)

Cnceptual Theme: Exploring Data: Describing patterns and departures from patterns

Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course provides instruction with appropriate emphasis on anticipating patterns. The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations.

 

Skills:

 Understand that the true regression line does not fit the population data perfectly, but rather is an idealized summary of that data.

 Know how to examine your data and a scatterplot of y vs. x for violations of assumptions that would make inference for regression unwise or invalid.

 Know how to examine displays of residuals from a regression to double check that conditions required for regression have been met.

 Know how to judge linearity and constant variance from a scatterplot of residuals against predicted values.

 Know how to judge Normality from a histogram and from a Normal probability plot.

 Remember to search for patterns, examine scatterplots both x against time and of the residuals against time.

 Know how to test the standard hypothesis that the true regression slope is 0.

 Know where to find relevant numbers in standard computer regression output.

 Be able to find a confidence interval for the slope of a regression based on the values reported in a standard regression output table.

 Be able to summarize a regression line.

 B able to state the meaning of the true regression slope, the standard error of the estimate slope, and the standard deviation of the errors.

 Be able to interpret the P-value of the t-statistic for the slope to test the standard null hypothesis.

 Be able to interpret a confidence interval for the slope of a regression.

Exercises: See Chapter 27 Exercises to be completed

Chapter 27 Quiz

Technology: Testing hypothesis about the association; creating confidence intervals for the slope; checking residual graphs using the TI-83/software; ActivStats lesson27: inference for regression

TEST: UNIT VII 29

 

Review for AP Exam (Class Days 20)

Conceptual Theme: Exploring Data: Describing patterns and departures from patterns

Conceptual Theme: Anticipating Patterns: Exploring random phenomena using probability and simulation

Conceptual Theme: Statistical Inference: Estimating population parameters and testing hypotheses

Conceptual Theme: Sampling and Experimentation: Planning and conducting a study

Curricular Requirements: The course provides instruction with appropriate emphasis on exploring data. The course provides instruction with appropriate emphasis on anticipating patterns. The course provides instruction with appropriate emphasis on statistical inference. The course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. The course teaches students how to communicate methods, results, and interpretations using the vocabulary of statistics. The course teaches students how to use graphing calculators and demonstrates the use of computers and/or computer output to enhance the development of statistical understanding through exploration and analysis of data, assessment of models, and simulations

 

Students will be given practice model exams from AP Central and from James Bohan’s preparation book: AP Statistics: Preparing for the Advanced Placement Examination. New York: Amsco School Publications, Inc., 2006.

Final Project (Class Days 20 Days) 30

Note: The practice exercises at the end of each chapter and the Investigative Tasks I will refer to by the name that Bock labeled the problem instead of referring to them by specific numbers – This is helpful when textbook editions change I can keep track of the problems going from an older version of the text to a newer edition.

 


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