AP STATISTICS Unit 8: Estimating with Confidence
Enduring understanding (Big Idea): Students will understand that inference is based on chance and that confidence
intervals are effective tools for estimating unknown parameters.
Essential Questions: 1. What is a confidence interval? 2. How do you interpret a confidence interval? 3. How do you
interpret the confidence level?
BY THE END OF THIS UNIT:
Students will know…
Students will be able to…
(Relationship to the AP Statistics Course Description)
III. Anticipating patterns: exploring random phenomena using probability and
simulation.
D. Sampling distributions
7. t-distribution
IV. Statistical inference: estimating population parameters and testing hypotheses
A. Estimation (point estimators and confidence intervals)
1. Estimating population parameters and margins of error
2. Properties of point estimators, included unbiasedness and variability
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
6. Confidence interval for a mean


Construct and interpret confidence intervals for a population
proportion p and a population mean µ.
Determine the sample size for a given margin of error,
confidence level, and the proportion of successes.
Vocabulary:
point estimator, point estimate, confidence interval, critical value, margin of
error, confidence level, standard error, robust
Unit Resources
Learning Tasks:
Performance Task:
Released AP Questions – 2000 #2, #6, 2002 #1, 2002B #4, 2003
# 6, 2003B #6, 2005 #5, 2008B #3, 2010 #3, 2010B #4, 2011 #6, 2011B #5
Unit Review Game: Jeopardy flipchart
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 8: Estimating with Confidence
CORE CONTENT
Clusters: Understand and evaluate random processes underlying statistical experiments; Make inferences and justify conclusions from
sample surveys, experiments, and observational studies.
Standard
 CCSS S-IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that
population.
 CCSS S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of
simulation for random sampling.
 CCSS S-IC.6 Evaluate reports based on data
 NCSCOS 3.09 Recognize, construct and interpret results using confidence intervals in the context of a problem.
Concepts and Skills to Master
 Interpret a confidence interval in context.
 Understand that a confidence interval gives a range of plausible values for the parameter
 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.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Sampling distributions, Normal distributions
Academic Vocabulary
Parameter, statistic, sampling distribution, unbiased estimator, variability of a statistic
Resources
 ACTIVITY Good Books (Platinum Resource Binder) or The mystery
mean or The mystery proportion (textbook p. 468)
 Textbook Correlation:
 Discuss the meaning of a point estimate.
Chapter 8 Introduction
Section 8.1 Confidence Intervals: The Basics
 Introduce the idea of a confidence interval.
 Talk about how to interpret confidence levels and confidence intervals.
 ACTIVITY The Confidence Interval applet
(http://bcs.whfreeman.com/tps4e/#628644__666391__)
 Discuss the conditions for constructing a confidence interval.
Sample Formative Assessment Tasks
Skill-based task
Problem Task
CHECK YOUR UNDERSTANDING (textbook page 476)
FRQ’s: 2002 – Q1
Sug gested I nstructio nal Strategies
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 8: Estimating with Confidence
CORE CONTENT
Cluster Title: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard
 CCSS S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation
for random sampling.
 CCSS S-IC.6 Evaluate reports based on data
 NCSCOS 3.09 Recognize, construct and interpret results using confidence intervals in the context of a problem.
Concepts and Skills to Master
 Construct and interpret a confidence interval for a population proportion.
 Determine critical values for calculating a confidence interval using a table or calculator.
 Carry out the steps in constructing a confidence interval for a population proportion.
 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 level of confidence C.
 Understand why each of the three inference conditions – Random, Normal, and Independent – is important.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
How to interpret confidence levels and confidence intervals
Academic Vocabulary
Standard error
Suggested Instructional Strategies
 ACTIVITY The beads or ALTERNATE ACTIVITY The pennies or Hershey’s
Kisses Activity (Platinum Resource Binder)
 Discuss what conditions need to be checked when calculating a confidence
interval for a population proportion.
 Introduce confidence levels other than 95% and how to calculate the critical
values for these confidence intervals.
 Discuss the four-step process used to calculate and interpret confidence intervals.
 Discuss how to choose an appropriate sample size based on the confidence level,
the proportion of successes, and the desired margin of error.
Sample Formative Assessment Tasks
Skill-based task
CHECK YOUR UNDERSTANDING (textbook pages 487, 490, 494)
Resources

Textbook Correlation:
Section 8.2 Estimating a Population Proportion
Problem Task
FRQ’s: 2000 – Q6, 2002B – Q4, 2003 – Q6, 2003B – Q6, 2005
– Q5, 2010- Q3, 2010B – Q4, 2011 – Q6, 2011B – Q5
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 8: Estimating with Confidence
CORE CONTENT
Cluster Title: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard

CCSS S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of
simulation for random sampling.
 CCSS S-IC.6 Evaluate reports based on data
 NCSCOS 3.09 Recognize, construct and interpret results using confidence intervals in the context of a problem.
Concepts and Skills to Master





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.
Determine sample statistics from a confidence interval.
Understand why each of the three inference conditions – Random, Normal, and Independent – is important.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
How to interpret confidence levels and confidence intervals
Academic Vocabulary
Standard error of the sample mean, degrees of freedom, robust procedures
Suggested Instructional Strategies
 Discuss the one-sample z interval for a population mean when σ is
known and discuss how to find the sample size.
 Introduce the t-distribution with ACTIVITY Calculator bingo or
Simulating Confidence Intervals with a Graphing Calculator
(Platinum Resource Binder).
 Compare the conditions needed when calculating a confidence
interval for a population proportion with a population mean.
 Discuss the idea of a robust procedure.
Sample Formative Assessment Tasks
Skill-based task
CHECK YOUR UNDERSTANDING (textbook pages 501, 507, 511)
Resources
 Textbook Correlation:
Section 8.3 Estimating a Population Mean
Problem Task
FRQ’s: 2000 – Q2, 2006B – Q3
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.