AP Statistics Proposed Syllabus -  Semester 2

 

COURSE DESCRIPTION:

 

AP Statistics is the high school equivalent of a one semester, introductory college statistics

course. In this course, students develop strategies for collecting, organizing, analyzing, and

drawing conclusions from data. Students design, administer, and tabulate results from surveys

and experiments. Probability and simulations aid students in constructing models for chance

behavior. Sampling distributions provide the logical structure for confidence intervals and

hypothesis tests. Students use a TI-83/84 graphing calculator or a TI Nspire, Fathom, statistical

software with a selection of statistics activities, and Web-based java applets to investigate statistical concepts. The teacher has a SmartBoard and TI SmartView, TI Nspire software, and Fathom to use for demonstration purposes and to instruct students how to use the different forms of technology. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.

 

COURSE GOALS:

In AP Statistics, students are expected to learn

Skills

To produce convincing oral and written statistical arguments, using appropriate

terminology, in a variety of applied settings.

When and how to use technology to aid them in solving statistical problems

Knowledge

Essential techniques for producing data (surveys, experiments, observational studies),

analyzing data (graphical & numerical summaries), modeling data (probability, random

variables, sampling distributions), and drawing conclusions from data (inference

procedures – confidence intervals and significance tests)

Habits of mind

To become critical consumers of published statistical results by heightening their

awareness of ways in which statistics can be improperly used to mislead, confuse, or

distort the truth.

Course Materials

Primary Text

TPS4 - Starnes, Yates and Moore. The Practice of Statistics, Fourth Edition. New York, NY: W H Freeman and Company, 2012. ISBN 978-1-4292-6258-3.

References, Resource Materials and Their Labels

 

BVD - Bock, Velleman and DeVeaux. Stats Modeling the World, Second Edition(AP Edition). Boston, MA: Pearson Education, Inc., 2007.

 

TPS- TTR - Tabor and Brown. The Practice of Statistics, Fourth Edition. Teacher’s Titanium Resource Binder. New York, NY: W H Freeman and Company, 2011.

 

CBWH - CollegeBoard. AP Statistics, Workshop Handbook, 2011-2012.

 

ABS -  Scheaffer, Gnandesikan, Watkins and Witmer. Activity-Based Statistics. New York, NY: Springer – Verlag, 1996.

 

WKST - Rossman, Chance and Oehsen. Workshop Statistics: Discovery with Data and the Graphing Calculator, Third Edition. Hoboken, NJ: John Wiley & Sons, Inc., 2008.

 

TPS – FG - Erickson, Tim. The Fathom Guide for The Practice of Statistics, Third Edition. New York, NY: W H Freeman and Company, 2008.

 

Spiegel and Stephens. Statistics, Fourth Edition. New York, NY: McGraw-Hill, 2011.

 

TPS3 -Yates, Moore & Starnes. The Practice of Statistics, 3d edition, W.H. Freeman, 2006.

 

TPS2 - Yates, Moore & Starnes. The Practice of Statistics, 2nd edition, W.H. Freeman, 2003.

 

KL-APSO -  Kucera, Lee. Instuctor for the Course: Y2984: Teaching AP* Statistics (Online) X 394.18 (Summer 2012).  Notes, activities and other instructional materials.

 

APP - Internet applets on various university and other sites.

F - Fathom, Release 2. Key Curriculum Press, Berkeley, CA.

NB3R - Curriculum List/Guide to all NUMB3Rs episodes complete with TI Worksheets and Activities.

TI-83+, TI-84, TI-84+ graphing calculators and Graph View Software.

 TI Nspire CAS Teacher Software

 

Timeline for Fall Semester/Spring Semester

Both semesters are based upon 55 minute class sessions. Because classes are taught on a college schedule, AP Statistics will only meet class sessions Monday, Wednesday and Friday. This breaks down into 50 sessions per semester. Every weekday evening, except Friday, tutorials are held from 7-9pm. I intend to schedule review sessions for Midterms/Finals and AP review during evening tutorials to make up time needed.

SEMESTER 2

 

Chapter

Class Sessions

7

7

8

7

9

8

10

8

11

6

12

7

Review for AP

10

TOTAL

110

 

SEMESTER TWO

Chapter 7

Day

Topics

Objectives: Students will be able to…

AP Course Obj

1

ACT

Tech

Jan.4

Introduction: German Tank Problem TPS- TTR 

 7.1 Parameters and Statistics 

Technology: Using Fathom to Simulate Sampling Distributions

·         Distinguish between a parameter and a statistic.

IIID. Sampling distributions

2

7.1 Sampling Variability, Describing Sampling Distributions

·         Understand the definition of a sampling distribution.

·         Distinguish between population distribution, sampling distribution, and the distribution of sample data.

·         Determine whether a statistic is an unbiased estimator of a population parameter.

·         Understand the relationship between sample size and the variability of an estimator.

IIID.

6. Simulation of sampling distributions

 

3

Tech

 

7.2 The Sampling Distribution of , Using the Normal Approximation for ,

Technology: Using an Applet to

Simulate the distribution of ˆp .

 

Activity: The Candy Machine.

·         Find the mean and standard deviation of the sampling distribution of a sample proportion  for an SRS of size n from a population having proportion p of successes.

·         Check whether the 10% and Normal conditions are met in a given setting.

·         Use Normal approximation to calculate probabilities involving .

·         Use the sampling distribution of  to evaluate a claim about a population proportion.

IIID.

1. Sampling distribution of a sample proportion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. Sampling distribution of a sample mean

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. Central Limit Theorem

 

4

Tech

7.3 The Sampling Distribution of : Mean and Standard Deviation, Sampling from a Normal Population

 

Technology: Using an Applet to

Simulate the distribution of x .

 

·         Find the mean and standard deviation of the sampling distribution of a sample mean  from an SRS of size n.

·         Calculate probabilities involving a sample mean  when the population distribution is Normal.

 

 

 

 

 

 

5

P

Tech

 

 

 

 

 

 

 

7.3  The Central Limit Theorem

 

Project: Sampling Distribution Simulation (CLT Simulation by J Tabor) Students will submit a typed, double-spaced report which includes complete responses to all items in the handout and a discussion of why statisticians prefer the mean as a measure of center instead of median.

 

 

 

 

 

 

 

·         Explain how the shape of the sampling distribution of  is related to the shape of the population distribution.

·         Use the central limit theorem to help find probabilities involving a sample mean .

6

Chapter 7 Review                                         Chapter 7 Review Exercises

7

Chapter 7 Test

Cumulative AP Practice Test 2

 

Chapter 8

Day

Topics

Objectives: Students will be able to:

AP Course Obj

1

Tech

8.1 The Idea of a Confidence Interval, Interpreting Confidence Levels and Confidence Intervals, Constructing a Confidence Interval

 

Technology: Simulating Confidence Intervals with

the Confidence Interval Applet

·         Interpret a confidence level.

·         Interpret a confidence interval in context.

·         Understand that a confidence interval gives a range of plausible values for the parameter.

IV. Statistical Inference: Estimating population parameters and testing hypotheses (30%-40%)

Statistical inference guides the selection of appropriate models.

 

A. Estimation (point estimators and confidence intervals)

 

1. Estimating population parameters and margins of error

 

2. Properties of point estimators, including unbiasedness and variability

 

2

8.1 Using Confidence Intervals Wisely, 8.2 Conditions for Estimating p, Constructing a Confidence Interval for p

·         Understand why each of the three inference conditions—Random, Normal, and Independent—is important.

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

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

·         Determine critical values for calculating a confidence interval using a table or your calculator.

3

Tech

8.2 Putting It All Together: The Four-Step Process, Choosing the Sample Size

 

Technology: Confidence Intervals

for p on the Calculator

·         Carry out the steps in constructing a confidence interval for a population proportion: define the parameter; check conditions; perform calculations; interpret results in context.

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

·         Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.

·         Understand why each of the three inference conditions—Random, Normal, and Independent—is important.

3. Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals

 

 

4. Large sample confidence interval for a proportion

 

4

Tech

8.3 When  Is Known: The One-Sample z Interval for a Population Mean, When  Is Unknown: The t Distributions, Constructing a Confidence Interval for

Technology: Inverse t on the

Calculator

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

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

·         Carry out the steps in constructing a confidence interval for a population mean: define the parameter; check conditions; perform calculations; interpret results in context.

 

 

 

6. Simulation of sampling distributions

 

 

 

 

 

7. t-distribution

 

5

Tech

F

8.3 Using t Procedures Wisely

 

Activity: Using Fathom to Investigate the Difference between z and t

·         Understand why each of the three inference conditions—Random, Normal, and Independent—is important.

6

Chapter 8 Review

·         Determine sample statistics from a confidence interval.

Chapter 8 Review Exercises

7

Chapter 8 Test

 

 

 

 

Chapter 9

Day

Topics

Objectives: Students will be able to:

AP Course Obj

1

9.1 The Reasoning of Significance Tests, Stating Hypotheses, Interpreting P-values, Statistical Significance

·         State correct hypotheses for a significance test about a population proportion or mean.

·         Interpret P-values in context.

IVB

1. Logic of significance testing, null and alternative hypotheses; p-values;

one- and two-sided tests; concepts of I and Type II errors; concept

of power

2

Tech

9.1 Type I and Type II Errors, Planning Studies: The Power of a Statistical Test

Technology: Investigating Power with an Applet

·         Interpret a Type I error and a Type II error in context, and give the consequences of each.

·         Understand the relationship between the significance level of a test, P(Type II error), and power.

15, 19, 21, 23, 25

3

Tech

9.2 Carrying Out a Significance Test, The One-Sample z Test for a Proportion

Technology: One-

Proportion z Test on the Calculator

·         Check conditions for carrying out a test about a population proportion.

·         If conditions are met, conduct a significance test about a population proportion.

 

IVB

2. Large sample test for a proportion

 

4

Tech

F

9.2 Two-Sided Tests, Why Confidence Intervals Give More Information

Technology: Tests and Confidence Intervals using Fathom

·         Use a confidence interval to draw a conclusion for a two-sided test about a population proportion.

5

Tech

9.3 Carrying Out a Significance Test for , The One Sample t Test, Two-Sided Tests and Confidence Intervals

Technology: Computing P-values from t Distributions on the Calculator, One Sample t Test on the Calculator

·         Check conditions for carrying out a test about a population mean.

·         If conditions are met, conduct a one-sample t test about a population mean .

·         Use a confidence interval to draw a conclusion for a two-sided test about a population mean.

IVB

 

4. Test for a mean

 

5. Test for a difference between two means (unpaired and paired)

 

6

9.3 Inference for Means: Paired Data, Using Tests Wisely

·         Recognize paired data and use one-sample t procedures to perform significance tests for such data.

7

Chapter 9 Review                                       Chapter 9 Review Exercises

8

Chapter 9 Test

 

 

 

 

 

Chapter 10

Day

Topics

Objectives: Students will be able to…

AP Course Obj

1

ACT

 

Activity: Is Yawning Contagious? TPS- TTR,

10.1 The Sampling Distribution of a Difference Between Two Proportions

·         Describe the characteristics of the sampling distribution of

·         Calculate probabilities using the sampling distribution of

IVB

 

3. Large sample test for a difference between two proportions

 

2

Tech

10.1 Confidence Intervals for p1p2

Technology: Confidence Intervals for a Difference in Proportions on the Calculator

·         Determine whether the conditions for performing inference are met.

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

3

NB3R

 

Tech

10.1 Significance Tests for p1p2, Inference for Experiments

 

Two-Proportion Z-test

episode #: 309 "Waste not"

 

Technology :Significance Tests for a Difference in Proportions on the Calculator

·         Perform a significance test to compare two proportions.

·         Interpret the results of inference procedures in a randomized experiment.

4

ACT

 

10.2 Activity: Does Polyester Decay? TPS- TTR, The Sampling Distribution of a Difference Between Two Means

·         Describe the characteristics of the sampling distribution of

·         Calculate probabilities using the sampling distribution of

IVB

 

5. Test for a difference between two means (unpaired and paired)

 

5

Tech

10.2 The Two-Sample t-Statistic, Confidence Intervals for

Technology: Confidence Intervals for a Difference in Means on the Calculator

·         Determine whether the conditions for performing inference are met.

·         Use two-sample t procedures to compare two means based on summary statistics.

·         Use two-sample t procedures to compare two means from raw data.

·         Interpret standard computer output for two-sample t procedures.

6

Tech

10.2 Significance Tests for , Using Two-Sample t Procedures Wisely

 

Technology: Two Sample t

Tests with Computer Software and Calculators

·         Perform a significance test to compare two means.

·         Check conditions for using two-sample t procedures in a randomized experiment.

·         Interpret the results of inference procedures in a randomized experiment.

7

Chapter 10 Review

·         Determine the proper inference procedure to use in a given setting.

Chapter 10 Review Exercises

P

 Project: Paper Airplanes TPS- TTR

MATERIALS: Two paper airplane pattern sheets, scissors, masking tape, tape measures,

graphing calculator

Don’t forget that templates are available at the website below!

http://www.funpaperairplanes.com/Plane%20Downloads.html

The purpose of this Activity is to see which of two paper airplane models—A or B—flies

farthest. Specifically, the object is to determine whether there is a significant difference in the

average distance flown for the two plane models.

1. As a class, design an experiment to determine which of the two paper airplane models

flies the farthest. Be sure to follow the principles of experimental design you learned in

Chapter 4.

2. State the hypotheses you are interested in testing.

3. Carry out your plan and collect the necessary data.

4. Compare the flight distances for the two models graphically and numerically. Does it

appear that the means are about the same, or is one mean different from the other?

5. Perform a significance test to determine if the difference in means is significant.

Use “Analyzing Experiments: A Template” TPS- TTR Submit a typed report analyzing the experiment, the decisions made, including answers to the 5 tasks, and a summary of conclusions with justification.

8

Chapter 10 Test                                  Cumulative AP Practice Test 3

 

Chapter 11

Day

Topics

Objectives: Students will be able to…

AP Course Obj

1

ACT

Tech

NB3R

 

Activity: The Candy Man Can TPS- TTR,

 

11.1 Comparing Observed and Expected Counts: The Chi-Square Statistic, The Chi-Square Distributions and P-values

 

Technology: Finding P-values

for Chi-Square Tests on the

Calculator

·         Know how to compute expected counts, conditional distributions, and contributions to the chi-square statistic.

·         Chi-square Test for Goodness-of-fit Episode #: 315 “End of Watch”

 

 

 

 

 

 

 

 

 

IVB

 

 

 

 

 

 

6. Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables)

 

 

2

Tech

11.1 The Chi-Square Goodness-of-Fit Test, Follow-Up Analysis

 

Technology: Chi-Square Goodness-of-Fit Tests on the Calculator

·         Check the Random, Large sample size, and Independent conditions before performing a chi-square test.

·         Use a chi-square goodness-of-fit test to determine whether sample data are consistent with a specified distribution of a categorical variable.

·         Examine individual components of the chi-square statistic as part of a follow-up analysis.

3

Tech

11.2 Comparing Distributions of a Categorical Variable, Expected Counts and the Chi-Square Statistic, The Chi-Square Test for Homogeneity, Follow-Up Analysis, Comparing Several Proportions

 

Technology: Chi-Square Tests for Two-Way Tables with Computer Software and Calculators

 

·         Check the Random, Large sample size, and Independent conditions before performing a chi-square test.

·         Use a chi-square test for homogeneity to determine whether the distribution of a categorical variable differs for several populations or treatments.

·         Interpret computer output for a chi-square test based on a two-way table.

·         Examine individual components of the chi-square statistic as part of a follow-up analysis.

·         Show that the two-sample z test for comparing two proportions and the chi-square test for a 2-by-2 two-way table give equivalent results.

4

ACT

 

11.2 The Chi-Square Test of Association/Independence, Using Chi-Square Tests Wisely

 

M&M’s: I Didn’t Get Enough Blues – Activity 13 from TPS 2nd ed.

X2 Goodness-of-Fit

·         Check the Random, Large sample size, and Independent conditions before performing a chi-square test.

·         Use a chi-square test of association/independence to determine whether there is convincing evidence of an association between two categorical variables.

·         Interpret computer output for a chi-square test based on a two-way table.

·         Examine individual components of the chi-square statistic as part of a follow-up analysis.

5

Chapter 11 Review

·         Distinguish between the three types of chi-square tests.

Chapter 11 Review Exercises

6

Chapter 11 Test

Two-Proportion Z-test

 

 

Chapter 12

Day

Topics

Objectives: Students will be able to…

AP Course Obj

1

ACT

 

Activity: The Helicopter Experiment TPS- TTR, 12.1 The Sampling Distribution of b, Conditions for Regression Inference

·         Check conditions for performing inference about the slope  of the population regression line.

 

 

 

 

 

 

 

IVB

 

 

 

7. Test for the slope of a least-squares regression line

 

2

Tech

12.1 Estimating Parameters, Constructing a Confidence Interval for the Slope

 

Technology: Regression

Inference using Computer Software and Calculators

·         Interpret computer output from a least-squares regression analysis.

·         Construct and interpret a confidence interval for the slope  of the population regression line.

3

12.1 Performing a Significance Test for the Slope

·         Perform a significance test about the slope  of a population regression line.

ACT

Tech

 

Skittleium –The decay of radioactive isotopes creates interesting data.  The isotope Skittleium is commonly found in vending machines throughout the world.  The final decay elements of Skittleium are Skittles.  This investigation leads into the reason for transformation of exponential and power functions.

4

Tech

12.2 Transforming with Powers and Roots

 

Technology: Transforming to Achieve Linearity on the Calculator

·         Use transformations involving powers and roots to achieve linearity for a relationship between two variables.

·         Make predictions from a least-squares regression line involving transformed data.

5

12.2 Transforming with Logarithms

·         Use transformations involving logarithms to achieve linearity for a relationship between two variables.

·         Make predictions from a least-squares regression line involving transformed data.

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

6

Chapter 12 Review                              Chapter 12 Review Exercises

7

Chapter 12 Test

Cumulative AP Practice Test 4

AP EXAM REVIEW: 5 DAYS  

SEMESTER 2 EXAM: Simulated AP format with Multiple Choice, Free Response

 

Final Project  The purpose of this project is for you to actually do statistics. You are to form a

hypothesis, design a study, conduct the study, collect the data, describe the data, and make

conclusions using the data. Use “Comments from Floyd Bullard”. To get your project approved, you must be able to demonstrate how your study will meet the requirements of the project. In other words, you need to clearly and completely communicate your hypotheses, your explanatory and response variables, the

test/interval you will use to analyze the results, and how you will collect the data so the conditions for inference will be satisfied. You must also make sure that your study will be safe and ethical if you are using human subjects. The proposal should be typed. If your proposal isn’t approved, you must resubmit the proposal for partial credit until it is approved. Each individual will be required to give a 5 minute oral presentation to the class.