Testing a Claim and Comparing Two Populations Or Groups

AP STATISTICS

(SECONDARY)

ESSENTIAL UNIT 7 (E07)

(TESTING A CLAIM AND COMPARING TWO POPULATIONS OR GROUPS)

(July 2012)

Unit Statement: In this unit the student will learn the basics of significance tests, will implement tests about a population proportion and a population mean. The student will also learn to compare two proportions and two means.

Essential Outcomes:(Assessed for Mastery)

The Student Will develop a correct hypotheses for a significance test about a population proportion or mean and interpret P-values in context.[9.1]

TSWinterpret and evaluate the consequences of a Type I error and a Type II error.[9.1]

TSWand explain the relationship between the significance level of a test, P(Type II error), and power.[9.1]

TSWcheck conditions for implementing a test about a population proportion and population mean,and if conditions are met, conduct a one-sample t test about a population proportion and mean. [9.2], [9.3]

TSWand use a confidence interval to draw a conclusion for a two-sided test about a population proportion and mean. [9.2], [9.3]

TSWRecognize paired data and use one-sample t procedures to perform significance tests for such data.[9.3]

TSWdescribe the characteristics and calculate probabilities using the sampling distribution of. [10.1]

TSWconstruct, interpret and perform a significance test of a confidence interval to compare two proportions. [10.1]

TSWdescribe the characteristics and calculate the probabilities of the sampling distribution of. [10.2]

TSWuse two-sample t procedures to compare two means from raw data, and interpret standard computer output for two-sample t procedures. [10.2]

TSWcheck conditions for using two-sample t procedures in a randomized experiment and determine the proper inference procedure to use in a given setting. [10.2]

Suggested Materials:

Text:The Practice of Statistics (4th edition), by Starnes, Yates, and Moore, W. H. Freeman & Co., 2012.

ISBN-13: 978-1-4292-4559-3, Instructor’s Resource Guide, The Practice of Statistics, Fourth Edition, 2012,

Graphing Calculator:TI-Nspire™ CX CAS

Graphing Technology Guide for Precalculus and Calculus, by Levy, published by Houghton Mifflin, 2001, ISBN 0-618-07287-X, Publisher’s Code 3-30431

TPS web site

4th edition:

3rd edition:

For practice of AP Statistics Exams, Section II (Free Response), past papers can be downloaded free from the College Board AP website:

From the above webpage, teachers should follow links to the Course Home Page for AP Statistics. In addition to past papers, this page contains a lot of helpful information about the course, including the most up-to-date Course Description.

There are vast sources of material for real life activities on websites such as:

AP Central: AP Statistics Course Home Page

Rossman and Chance’s java applets

ARTIST Assessment Resources

NCSSM Statistics Institutes

Jason Molesky’s StatsMonkey Page

Larry Green’s statistics review site

Against All Odds video series

Statistics video toolkit

Rice Virtual Lab in Statistics

The Data and Story Library

Exploring Data: Rex Boggs’ outstanding resources site in Australia

CAUSEWeb

Assignments:

[9.1]Page 546 - 549{1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25}

[9.2]Page 562 - 565{27–30, 41, 43, 45, 47, 49, 51, 53, 55}

[9.3]Page 587 - 593{57–60, 71, 73, 75, 77, 89, 94–97, 99–104}

Chapter 9 Review, Pg. 594 - 596 Chapter 9 Review Exercises

Chapter 9 Test

[10.1]Page 621 - 626{1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 23}

[10.2]Page 652 - 660{29-32, 35, 37, 57, 39, 41, 43, 45,51, 53, 59, 65, 67-70}

Chapter 10 Review, Pg. 661 - 664 Chapter 10 Review Exercises

Chapter 10 Test 33R, 34 R, 75 R, 76 R

RUBRICS AND PACING CHARTS FOUND ON FOLLOWING PAGES………………..

AP STATISTICS (SEC) E07

ESSENTIAL UNIT 7 (E07)

RUBRIC

Exploring Data

(JULY 2012)

‘A’ Level Mastery / ‘B’ Level Mastery / ‘P’ in progress
TSW #1
[9.1] / Interprets P-values in context. / States correct hypotheses for a significance test about a population proportion or mean. / B Level Not Achieved.
TSW #2
[9.1] / Interprets a Type I error and a Type II error in context and give the consequences of each. / B Level Not Achieved.
TSW 3
[9.1] / Explains the relationship between the significance level of a test, P (Type II error), and power.
TSW #4
[9.2] / Checks conditions for implementing a test about a population proportion.
Conducts a one-sample t test about a population proportion and mean, if conditions are met. / B Level Not Achieved.
TSW #5
[9.2], [9.3] / Uses a confidence interval to draw a conclusion for a two-sided test about a population proportion and mean.
TSW #6
[9.3] / Recognizes paired data and use one-sample t procedures to perform significance tests for such data. / B Level Not Achieved.
TSW #7
[10.1] / Describes the characteristics of the sampling distribution.
Calculates probabilities using the sampling distribution of. / B Level Not Achieved.
TSW #8
[10.1] / Interprets a confidence interval to compare two proportions.
Interprets the results of inference procedures in a randomized experiment. / Determines whether the conditions for performing inference are met.
Constructs a confidence interval to compare two proportions.
Performs a significance test to compare two proportions. / B Level Not Achieved.
TSW #9
[10.2] / Interprets the mean and standard deviation of a binomial random variable in context.
Determines whether the conditions for performing inference are met. / Describes the characteristics of the sampling distribution of.
Calculates probabilities using the sampling distribution of . / B Level Not Achieved.
TSW #10
[10.2] / Uses two-sample t procedures to compare two means based on summary statistics. / Uses two-sample t procedures to compare two means from raw data.
Performs a significance test to compare two means. / B Level Not Achieved.
TSW #11
[10.2] / Interprets the results of inference procedures in a randomized experiment.
Determines the proper inference procedure to use in a given setting. / Checksconditions for using two-sample t procedures in a randomized experiment. / B Level Not Achieved.

To receive an ‘A’, the student must show ‘A’ level mastery in 8 out of 10 of the ‘A’ level categories.

AP STATISTICS

RUBRIC FOR

ESSENTIAL UNIT 6 (E06)

Name______Date ______

‘A’ = / To earn an A for the unit, the student will have all of the B’s marked as well as two or more A’s.
‘B’ = / To earn a B for the unit, the student will have all of the B’s marked and one or no A’s marked.
‘IP’ = / If even one box in the IP column is marked, the grade is ‘In Progress’
‘A’ / ‘B’ / ‘IP’
TSW 1 / States correct hypotheses for a significance test about a population proportion or mean.
Interprets P-values in context.
TSW 2 / Interprets a Type I error and a Type II error in context and give the consequences of each.
TSW 3 / Explains the relationship between the significance level of a test, P (Type II error), and power.
TSW 4 / Checks conditions for implementing a test about a population proportion.
Conducts a one-sample t test about a population proportion, if conditions are met.
TSW 5 / Uses a confidence interval to draw a conclusion for a two-sided test about a population proportion.
TSW 6 / Recognizes paired data and use one-sample t procedures to perform significance tests for such data.
Uses a confidence interval to draw a conclusion for a two-sided test about a population mean.
TSW 7 / Describes the characteristics of the sampling distribution
Calculates probabilities using the sampling distribution of.
TSW 8 / Determines whether the conditions for performing inference are met.
Constructs a confidence interval to compare two proportions.
Performs a significance test to compare two proportions.
Interprets a confidence interval to compare two proportions.
Interprets the results of inference procedures in a randomized experiment.
TSW 9 / Describes the characteristics of the sampling distribution of.
Calculates probabilities using the sampling distribution of .
Interprets the mean and standard deviation of a binomial random variable in context.
Determines whether the conditions for performing inference are met.
TSW 10 / Uses two-sample t procedures to compare two means from raw data.
Performs a significance test to compare two means.
Uses two-sample t procedures to compare two means based on summary statistics.
TSW 11 / Checksconditions for using two-sample t procedures in a randomized experiment.
Interprets the results of inference procedures in a randomized experiment.
Determines the proper inference procedure to use in a given setting.

To receive an ‘A’, the student must show ‘A’ level mastery in 8 out of 10 of the ‘A’ level categories.

Unit Pace for Chapter 9

Day / Topics / Objectives: Students will be able to: / Homework
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.

/ 1, 3, 5, 7, 9, 11, 13
2 / 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 / 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.

/ 27–30, 41, 43, 45
4 / 9.2 Two-Sided Tests, Why Confidence Intervals Give More Information, Technology: Tests and Confidence Intervals using Minitab /

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

/ 47, 49, 51, 53, 55
5 / 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.

/ 57–60, 71, 73
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.

/ 75, 77, 89, 94–97, 99–104
7 / Chapter 9 Review / Chapter 9 Review Exercises
8 / Chapter 9 Test

Unit Pace for Chapter 10

Day / Topics / Objectives: Students will be able to… / Homework
1 / Activity: Is Yawning Contagious?, 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

/ 1, 3, 5
2 / 10.1 Confidence Intervals for p1 – p2 , 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.

/ 7, 9, 11, 13
3 / 10.1 Significance Tests for p1 – p2, Inference for Experiments, 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.

/ 15, 17, 21, 23
4 / 10.2 Activity: Does Polyester Decay?, The Sampling Distribution of a Difference Between Two Means /

Describe the characteristics of the sampling distribution of
Calculate probabilities using the sampling distribution of

/ 29-32, 35, 37, 57
5 / 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.

/ 39, 41, 43, 45
6 / 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.

/ 51, 53, 59, 65, 67-70
7 / Chapter 10 Review /

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

/ Chapter 10 Review Exercises
8 / Chapter 10 Test / 33R, 34 R, 75 R, 76 R

AP STATISTICS (SEC) E07