ADVANCED PLACEMENT CALCULUS AB

ADVANCED PLACEMENT STATISTICS COURSE SYLLABUS

OVERVIEW

Advanced Placement Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data through four broad themes: (1) exploring data, (2) sampling and experimentation, (3) anticipating patterns and, (4) statistical inference. Collaboration between the students, parents, and classroom teacher will go in effect to produce a calendar for extended sessions. A minimum of five (5) sessions, including a mock exam, are required in order to cover all objectives necessary to help be successful on the exam.

TEACHING STRATEGIES

It is understood that the prerequisites for Advanced Placement Statistics expose student the TI-83 or 84 calculators. Most students own the TI-83 plus, TI-84, or the TI-89. Other students are encouraged to purchase the TI-84 or TI-89. In addition to the calculator, students will have the opportunity to see a set of interactive statistical applets and software including Fathom. Students will also learn the strategy and not just the skills. At various concepts special problems will be assigned to help give students experience using a representative statistics package and writing statistics narratives. Students must be able to speak statistically and convey data within context. It is my belief that students can successfully present information verbally in comfortable settings. Students are seated in pods from three (3) to six (6) students each creating open opportunities for collaborative work. All tests are formatted like the Advanced Placement exam. This allows the students to become familiar with what to expect. Students are also expected to remediate and correct all tests if necessary. Test corrections, if necessary, are mandatory and will be 5% of the final grade. All test corrections must be completed within two weeks of the date of return.

CLASSROOM MECHANICS

Attendance: Please refer to the Weaver Academy attendance policy.

Make-Up Work: Any work that is missed due to an absence must be completed within 3 school days of the absence.

Tutorials: Any student that earns a “C” or lower on any progress report is required to attend tutorial for AP Statistics. Please refer to your individual teacher for tutorial availability. WE are here to help each student succeed. WE will do whatever WE can to ensure that your child gets as much assistance with their education as possible.

Schedule─ Tuesdays: 4:05-5:00pm, other times by appointment only.

Course Assessment: We will use a variety of assessment tools throughout the course. Each quarter’s average will be calculated using the following percentages:

Remediation 5% Projects 10% Quizzes 35% Tests 50%

A test will be given at the end of each unit. Cumulative tests will also be given periodically throughout the course. Test corrections are calculated in the Remediation score.

Late Work: No late work will be accepted with the exception of absences. Students are only allowed to turn in late work if they are absent the day the work is assigned.

Grading Scale: 90 – 100 A 60 – 69 D 80 – 89 B 0 – 59 F 70 – 79 C **Normal rounding rules will apply**

Your final grade in this course will be comprised of your Quarter 3 and Quarter 4 averages (80%) and the End of Course Exam (20%).

Emergency Procedures: During a fire drill please walk orderly out the double doors to the parking lot across from the mobile units. If a fire drill occurs during lunch please find your third period teacher in the appointed area. During a tornado drill please walk orderly out the double doors to the north wing or the main building. We will enter from the garage or the Auto Shop. During lockdown please find a place on the floor as far as possible from the door/windows and keep quiet to be able to hear all directions from the teacher. If lockdown occurs during lunch, please go to the nearest faculty/staff location.

Honor Pledge: I will abide by the Weaver Honor Code. I will not give or receive unpermitted assistance in the preparation of any work or assessment that is to be used by the instructor as the basis of grading. WE expect every student to keep a copy of this syllabus in their notebook so we can refer to it when necessary. If you have any questions regarding the items discussed in this syllabus, please ask immediately.

CONTACT INFORMATION: Ms. Nina Sumpter P. 336.370.8282ex1743 Voicemail#: 206863 Email: [email protected]

Texting App: Remind- Enter this number 81010, Text this message @589apstats Or email [email protected] (subject line can be blank)

mailto:[email protected]

mailto:[email protected]

Pacing Guide (Tentative Schedule-follows the online book edition) An overview of the course will be given the first day.

Unit Name Description Objectives Covered

Unit 3: Anticipating Patterns Days (approximately) Block—6 Yearlong—11

Chapter 5: Probability What are the chances? 5.1 Introduction, The Idea of Probability,

Myths about Randomness

5.1 Simulation

5.2 Probability Models, Basic Rules of

Probability

5.2 Two-Way Tables and Probability, Venn

Diagrams and Probability

5.3 What is Conditional Probability?,

Conditional Probability and Independence,

Tree Diagrams and the General Multiplication

Rule

5.3 Independence: A Special Multiplication

Rule, Calculating Conditional Probabilities

o Interpret probability as a long-run

relative frequency.

o Use simulation to model chance

behavior.

o Describe a probability model for a

chance process.

o Use basic probability rules, including the

complement rule and the addition rule

for mutually exclusive events.

o Use a Venn diagram to model a chance

process involving two events.

o Use the general addition rule to calculate

P(AB)

o When appropriate, use a tree diagram to

describe chance behavior.

o Use the general multiplication rule to

solve probability questions.

o Determine whether two events are

independent.

o Find the probability that an event occurs

using a two-way table.

o When appropriate, use the multiplication

rule for independent events to compute

probabilities.

o Compute conditional probabilities.

Unit 1: Exploring Data Days (approximately) Block—6 Yearlong—11

Chapter 1: Exploring Data 1.1 Bar Graphs and Pie Charts, Graphs: Good

and Bad

1.1 Two-Way Tables and Marginal

Distributions, Relationships Between

Categorical Variables: Conditional

Distributions, Organizing a Statistical Problem

1.2 Dotplots, Describing Shape, Comparing

Distributions, Stemplots

1.2 Histograms, Using Histograms Wisely

1.3 Measuring Center: Mean and Median,

Comparing Mean and Median, Measuring

Spread: IQR, Identifying Outliers

1.3 Five Number Summary and Boxplots,

Measuring Spread: Standard Deviation,

Choosing Measures of Center and Spread

o Identify the individuals and variables in

a set of data.

o Classify variables as categorical or

quantitative. Identify units of

measurement for a quantitative variable.

o Make a bar graph of the distribution of a

categorical variable or, in general, to

compare related quantities.

o Recognize when a pie chart can and

cannot be used.

o Identify what makes some graphs

deceptive.

o From a two-way table of counts, answer

questions involving marginal and

conditional distributions.

o Describe the relationship between two

categorical variables by computing

appropriate conditional distributions.

o Construct bar graphs to display the

relationship between two categorical

variables.

o Make a dotplot or stemplot to display

small sets of data.

o Describe the overall pattern (shape,

center, and spread) of a distribution and

identify any major departures from the

pattern (like outliers).

o Identify the shape of a distribution from

a dotplot, stemplot, or histogram as

roughly symmetric or skewed. Identify

the number of modes.

o Make a histogram with a reasonable

choice of classes.

o Identify the shape of a distribution from

a dotplot, stemplot, or histogram as

roughly symmetric or skewed. Identify

the number of modes.

o Interpret histograms.

o Calculate and interpret measures of

center (mean, median)


spread (IQR)

o Identify outliers using the 1.5 IQR

rule.

o Make a boxplot.


spread (standard deviation)

o Select appropriate measures of center

and spread

o Use appropriate graphs and numerical

summaries to compare distributions of

quantitative variables.


Chapter 2: Modeling Distributions of Data 2.1 Introduction, Measuring Position:

Percentiles, Cumulative Relative Frequency

Graphs, Measuring Position: z-scores

2.1 Transforming Data, Density Curves

2.2 Normal Distributions, The 68-95-99.7

Rule, The Standard Normal Distribution

2.2 Normal Distribution Calculations

2.2 Assessing Normality

o Use percentiles to locate individual

values within distributions of data.

o Interpret a cumulative relative frequency

graph.

o Find the standardized value (z-score) of

an observation. Interpret z-scores in

context.

o Describe the effect of adding,

subtracting, multiplying by, or dividing

by a constant on the shape, center, and

spread of a distribution of data.

o Approximately locate the median (equal-

areas point) and the mean (balance point)

on a density curve.

o Use the 68–95–99.7 rule to estimate the

percent of observations from a Normal

distribution that fall in an interval

involving points one, two, or three

standard deviations on either side of the

mean.

o Use the standard Normal distribution to

calculate the proportion of values in a

specified interval.

o Use the standard Normal distribution to

determine a z-score from a percentile.

o Use Table A to find the percentile of a

value from any Normal distribution and

the value that corresponds to a given

percentile.

o Make an appropriate graph to determine

if a distribution is bell-shaped.

o Use the 68-95-99.7 rule to assess

Normality of a data set.

o Interpret a Normal probability plot


Chapter 3: Describing Relationships 3.1 Explanatory and response variables

3.1 Displaying relationships: scatterplots

3.1 Interpreting scatterplots

3.1 Measuring linear association: correlation

3.1 Facts about correlation

3.2 Least-squares regression

3.2 Interpreting a regression line

3.2 Prediction

3.2 Residuals and the least-squares regression

line

3.2 Calculating the equation of the least-

squares regression line

3.2 How well the line fits the data: residual

plots

3.2 How well the line fits the data: the role of

r2 in regression

3.2 Interpreting computer regression output

3.2 Correlation and regression wisdom

o Describe why it is important to

investigate relationships between

variables.

o Identify explanatory and response

variables in situations where one

variable helps to explain or influences

the other.

o Make a scatterplot to display the

relationship between two quantitative

variables.

o Describe the direction, form, and

strength of the overall pattern of a

scatterplot.

o Recognize outliers in a scatterplot.

o Know the basic properties of correlation.

o Calculate and interpret correlation.

o Explain how the correlation r is

influenced by extreme observations.

o Interpret the slope and y intercept of a

least-squares regression line.

o Use the least-squares regression line to

predict y for a given x.

o Explain the dangers of extrapolation.

o Calculate and interpret residuals.

o Explain the concept of least squares.

o Use technology to find a least-squares

regression line.

o Find the slope and intercept of the least-

squares regression line from the means

and standard deviations of x and y and

their correlation.

o Construct and interpret residual plots to

assess if a linear model is appropriate.

o Use the standard deviation of the

residuals to assess how well the line fits

the data.

o Use r2 to assess how well the line fits the

data.

o Identify the equation of a least-squares

regression line from computer output.

o Explain why association doesn’t imply

causation.

o Recognize how the slope, y intercept,

standard deviation of the residuals, and

r2 are influenced by extreme

observations.


Chapter 6: Random Variables 6.1 Standard Deviation (and Variance) of a

Discrete Random Variable, Continuous

Random Variables

6.2 Linear Transformations

6.2 Combining Random Variables, Combining

Normal Random Variables

6.3 Binomial Settings and Binomial Random

Variables, Binomial Probabilities

6.3 Mean and Standard Deviation of a

Binomial Distribution, Binomial Distributions

in Statistical Sampling

6.3 Geometric Random Variables

o Use a probability distribution to answer

questions about possible values of a random

variable.

o Calculate the mean of a discrete random

variable.

o Interpret the mean of a random variable.

o Calculate the standard deviation of a discrete

random variable.

o Interpret the standard deviation of a random

variable.

o Describe the effects of transforming a

random variable by adding or subtracting a

constant and multiplying or dividing by a

constant.

o Find the mean and standard deviation of the

sum or difference of independent random

variables.

o Determine whether two random variables are

independent.

o Find probabilities involving the sum or

difference of independent Normal random

variables.

o Determine whether the conditions for a

binomial random variable are met.

o Compute and interpret probabilities involving

binomial distributions.

o Calculate the mean and standard deviation of

a binomial random variable. Interpret these

values in context.

o Find probabilities involving geometric

random variables.


Chapter 7: Sampling Distributions 7.1 Parameters and Statistics

7.1 Sampling Variability, Describing Sampling

Distributions

7.2 The Sampling Distribution of p̂ , Using

the Normal Approximation for p̂ ,

7.3 The Sampling Distribution of x : Mean

and Standard Deviation, Sampling from a

Normal Population

7.3 The Central Limit Theorem

o Distinguish between a parameter and a

statistic.

o Understand the definition of a sampling

distribution.

o Distinguish between population distribution,

sampling distribution, and the distribution of

sample data.

o Determine whether a statistic is an unbiased

estimator of a population parameter.

o Understand the relationship between sample

size and the variability of an estimator.


sampling distribution of a sample proportion

p̂ for an SRS of size n from a population

having proportion p of successes.

o Check whether the 10% and Normal

conditions are met in a given setting.

o Use Normal approximation to calculate

probabilities involving p̂ .

o Use the sampling distribution of p̂ to

evaluate a claim about a population

proportion.


sampling distribution of a sample mean x

from an SRS of size n.

o Calculate probabilities involving a sample

mean x when the population distribution is

Normal.

o Explain how the shape of the sampling

distribution of x is related to the shape of

the population distribution.

o Use the central limit theorem to help find

probabilities involving a sample mean x .

Unit 2: Sampling and Experimentation Days (approximately) Block—8 Yearlong—14

Chapter 4: Designing Studies 4.1 Introduction, Sampling and Surveys, How

to Sample Badly, How to Sample Well:

Random Samples

4.1 Other Sampling Methods

4.1 Inference for Sampling, Sample Surveys:

What Can Go Wrong?

4.2 Observational Studies vs. Experiments,

The Language of Experiments, How to

Experiment Badly

4.2 How to Experiment Well, Three Principles

of Experimental Design

4.2 Experiments: What Can Go Wrong?

Inference for Experiments

4.2 Blocking, Matched Pairs Design

4.3 Scope of Inference, the Challenges of

Establishing Causation

4.2 Class Experiments

or

4.3 Data Ethics* (*optional topic)

o Identify the population and sample in a

sample survey.

o Identify voluntary response samples and

convenience samples. Explain how these bad

sampling methods can lead to bias.

o Describe how to use Table D to select a

simple random sample (SRS).

o Distinguish a simple random sample from a

stratified random sample or cluster sample.

Give advantages and disadvantages of each

sampling method.

o Explain how undercoverage, nonresponse,

and question wording can lead to bias in a

sample survey.

o Distinguish between an observational study

and an experiment.

o Explain how a lurking variable in an

observational study can lead to confounding.

o Identify the experimental units or subjects,

explanatory variables (factors), treatments,

and response variables in an experiment.

o Describe a completely randomized design for

an experiment.

o Explain why random assignment is an

important experimental design principle.

o Describe how to avoid the placebo effect in

an experiment.

o Explain the meaning and the purpose of

blinding in an experiment.

o Explain in context what “statistically

significant” means.

o Distinguish between a completely

randomized design and a randomized block

design.

o Know when a matched pairs experimental

design is appropriate and how to implement

such a design.

o Determine the scope of inference for a

statistical study.

o Evaluate whether a statistical study has been

carried out in an ethical manner.

Unit 4: Statistical Inference Days (approximately) Block—5 Yearlong—10

Chapter 8: Estimating with Confidence 8.1 Using Confidence Intervals Wisely, 8.2

Conditions for Estimating p, Constructing a

Confidence Interval for p

8.2 Putting It All Together: The Four-Step

Process, Choosing the Sample Size

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

8.3 Using t Procedures Wisely

o Interpret a confidence level.

o Interpret a confidence interval in context.

o Understand that a confidence interval gives

a range of plausible values for the

parameter.

o Understand why each of the three inference

conditions—Random, Normal, and

Independent—is important.

o Explain how practical issues like

nonresponse, undercoverage, and response

bias can affect the interpretation of a

confidence interval.

o Construct and interpret a confidence interval

for a population proportion.

o Determine critical values for calculating a

confidence interval using a table or your

calculator.

o Carry out the steps in constructing a

confidence interval for a population

proportion: define the parameter; check

conditions; perform calculations; interpret

results in context.

o Determine the sample size required to obtain

a level C confidence interval for a

population proportion with a specified

margin of error.

o Understand how the margin of error of a

confidence interval changes with the sample

size and the level of confidence C.





for a population mean.

o Determine the sample size required to obtain

a level C confidence interval for a

population mean with a specified margin of

error.

o Carry out the steps in constructing a

confidence interval for a population mean:

define the parameter; check conditions;

perform calculations; interpret results in

context.




o Determine sample statistics from a

confidence interval.


Chapter 9: Testing a Claim 9.1 Type I and Type II Errors, Planning

Studies: The Power of a Statistical Test

9.2 Carrying Out a Significance Test, The

One-Sample z Test for a Proportion

9.2 Two-Sided Tests, Why Confidence

Intervals Give More Information

9.3 Carrying Out a Significance Test for ,

The One Sample t Test, Two-Sided Tests and

Confidence Intervals

9.3 Inference for Means: Paired Data, Using

Tests Wisely

o State correct hypotheses for a significance

test about a population proportion or mean.

o Interpret P-values in context.

o Interpret a Type I error and a Type II error

in context, and give the consequences of

each.

o Understand the relationship between the

significance level of a test, P(Type II error),

and power.

o Check conditions for carrying out a test

about a population proportion.

o If conditions are met, conduct a significance

test about a population proportion.

o Use a confidence interval to draw a

conclusion for a two-sided test about a

population proportion.

o Check conditions for carrying out a test

about a population mean.

o If conditions are met, conduct a one-sample

t test about a population mean .

o Use a confidence interval to draw a

conclusion for a two-sided test about a

population mean.

o Recognize paired data and use one-sample t

procedures to perform significance tests for

such data.


Chapter 10: Comparing Two Populations or Groups 10.1 Confidence Intervals for p1 – p2

10.1 Significance Tests for p1 – p2, Inference

for Experiments

10.2 Activity: Does Polyester Decay?, The

Sampling Distribution of a Difference Between

Two Means

10.2 The Two-Sample t-Statistic, Confidence

Intervals for 1 2

10.2 Significance Tests for 1 2

, Using

Two-Sample t Procedures Wisely

o Describe the characteristics of the sampling

distribution of 1 2ˆ ˆp p

o Calculate probabilities using the sampling

distribution of 1 2ˆ ˆp p

o Determine whether the conditions for

performing inference are met.


to compare two proportions.

o Perform a significance test to compare two

proportions.

o Interpret the results of inference procedures

in a randomized experiment.

o Describe the characteristics of the sampling

distribution of 1 2x x

o Calculate probabilities using the sampling

distribution of 1 2x x

o Determine whether the conditions for

performing inference are met.

o Use two-sample t procedures to compare

two means based on summary statistics.

o Use two-sample t procedures to compare

two means from raw data.

o Interpret standard computer output for two-

sample t procedures.

o Perform a significance test to compare two

means.

o Check conditions for using two-sample t

procedures in a randomized experiment.

o Interpret the results of inference procedures

in a randomized experiment.

o Determine the proper inference procedure to

use in a given setting.


Chapter 11: Inference for Distributions of Categorical Data 11.1 The Chi-Square Goodness-of-Fit Test,

Follow-Up Analysis

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

11.2 The Chi-Square Test of

Association/Independence, Using Chi-Square

Tests Wisely

o Know how to compute expected counts,

conditional distributions, and contributions

to the chi-square statistic.

o Check the Random, Large sample size, and

Independent conditions before performing a

chi-square test.

o Use a chi-square goodness-of-fit test to

determine whether sample data are

consistent with a specified distribution of a

categorical variable.

o Examine individual components of the chi-

square statistic as part of a follow-up

analysis.



chi-square test.

o Use a chi-square test for homogeneity to

determine whether the distribution of a

categorical variable differs for several

populations or treatments.

o Interpret computer output for a chi-square

test based on a two-way table.



analysis.

o 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.



chi-square test.

o Use a chi-square test of

association/independence to determine

whether there is convincing evidence of an

association between two categorical

variables.

o Interpret computer output for a chi-square

test based on a two-way table.



analysis.

o Distinguish between the three types of chi-

square tests.


Chapter 12: More About Regression 12.1 The Sampling Distribution of b,

Conditions for Regression Inference

12.1 Estimating Parameters, Constructing a

Confidence Interval for the Slope

12.1 Performing a Significance Test for the

Slope

12.2 Transforming with Powers and Roots

12.2 Transforming with Logarithms

o Check conditions for performing inference

about the slope of the population

regression line.

o Interpret computer output from a least-

squares regression analysis.


for the slope of the population regression

line.

o Perform a significance test about the slope

of a population regression line.

o Use transformations involving powers and

roots to achieve linearity for a relationship

between two variables.

o Make predictions from a least-squares

regression line involving transformed data.

o Use transformations involving logarithms to

achieve linearity for a relationship between

two variables.

o Make predictions from a least-squares

regression line involving transformed data.

o Determine which of several transformations

does a better job of producing a linear

relationship.

MAJOR ASSIGNMENTS

• CRITICAL STATISTICAL ANALYSES These assignments provide students the opportunity to find an article in print or electronic form that is based on a statistical procedure. Students use the tools they have learned in class to analyze the information in the article, and then write a critical report in their findings.

• RELEASED FREE RESPONSE QUESTIONS Certain questions will be assigned from 1993-current tests for students to complete as homework, class work, a quiz, or as part of a unit or cumulative test.

• FINAL PROJECT A team approach to designing and conducting a statistical study, with an extensive set of scoring rubrics.

• CHAPTER PROJECTS Students will complete certain chapter projects as a hands-on approach to learning concepts.

• UNIT TESTS There are four unit test and up to four cumulative AP test.

• CHAPTER QUIZZES Students will take multiple quizzes per chapter in a variety of forms including but not limited to vocabulary, reading, matching, case studies, released free response questions, etc. There will be one cumulative quiz per chapter.

MAJOR TEXT Yates, Daniel S., Moore, David S., and Starnes, Daren S. The Practice of Statistics, 4th ed. New York: W.H. Freeman, 2011 (online edition)

ADVANCED PLACEMENT CALCULUS AB

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