AP Statistics 554: 2015-16 Syllabus - Mr. Davis Math

advertisement
Bishop Walsh School
SY 2015-2016
AP Statistics Syllabus
Mr. Shane Davis
[email protected]
mrdavismathbw.weebly.com
Course Description:
The purpose of this course is to introduce students to the major concepts and tools for
collecting, analyzing, and drawing conclusions from data. Students are exposed to four
broad conceptual themes: exploring data, sampling and experimentation, anticipating
patterns, and statistical inference. This AP Statistics course is taught as an activitybased course in which students actively construct their own understanding of the
concepts and techniques of statistics through the use of small groups, projects, and
technology.
Course Textbook(s):
Bluman, Allan: Elementary Statistics: A Step-by-Step Approach, 7th edition.
New York: McGraw-Hill, 2009. ISBN: 978-0-07-353497
Hinders, Duane C.: 5 Steps to a 5: AP Statistics, 2016
New York: McGraw-Hill, 2015. ISBN: 978-0-07-184645-5
Technology:

All students need to have access to TI-83, TI-83 Plus, TI-84, TI-89, TI-nspire, or
TI-nspire CAS graphing calculators for use in class, at home, on any assignment
or assessment, and on the AP Exam. If purchasing a calculator for the first time,
then the TI-nspire CAS is strongly recommended for purchase. Students are
encouraged to use their calculator throughout the course and become familiar
with the keystrokes and underlying operations the calculator is computing.

All students will have access periodically to the computer lab to use statistical
software (Minitab, Excel) to aid in graphing, problem solving, and simulations.
S. Davis
1
Bishop Walsh School
SY 2015-2016
Course Outline:
Approximate
Time
Instruction:
2 weeks
Test:
1 day
Instruction:
2 weeks
Test:
1 day
S. Davis
Topics/Activities
Chapter 1: The Nature of Probability and Statistics
1.1 – Descriptive and Inferential Statistics
1.2 – Variables and Types of Data
1.3 – Data Collection and Sampling Techniques
 Random Sampling
 Systematic Sampling
 Stratified Sampling
 Cluster Sampling
 Other Sampling Methods
1.4 – Observational and Experimental Studies
1.5 – Uses and Misuses of Statistics
 Suspect Samples
 Ambiguous Averages
 Detached Statistics
 Implied Connections
 Misleading Graphs
 Faulty Survey Questions
1.6 – Computers and Calculators in Statistics
Chapter 2: Frequency Distributions and Graphs
2.1 – Organizing Data
 Categorical frequency distributions
 Grouped frequency distributions
2.2 – Histograms, Frequency Polygons, and Ogives
 Histogram
 Frequency polygon
 Ogive
 Relative frequency graphs
 Distribution shapes
2.3 – Other Types of Graphs
 Bar graphs
 Pareto charts
 Time series graph
 Pie graph
 Misleading graphs
 Stem and leaf plots
2
Bishop Walsh School
Instruction:
3 weeks
Test:
1 day
Instruction:
3 weeks
Test:
1 day
S. Davis
SY 2015-2016
Chapter 3: Data Description
3.1 – Measures of Central Tendency
 Mean
 Median
 Mode
 Midrange
 Weighted Mean
 Distribution shapes
3.2 – Measures of Variation
 Range
 Population variance and standard deviation
 Sample variance and standard deviation
 Variance and standard deviation for grouped data
 Coefficient of variation
 Range rule of thumb
 Chebyshev’s theorem
 The Empirical (Normal) Rule
3.3 – Measures of Position
 Standard scores
 Percentiles
 Quartiles and deciles
 Outliers
3.4 – Exploratory Data Analysis
 The Five-Number summary and boxplots
Chapter 4: Probability and Counting Rules
4.1 – Sample Spaces and Probability
 Classical Probability
 Complementary events
 Empirical probability
 Law of large numbers
 Subjective probability
4.2 – The Addition Rules of Probability
4.3 – The Multiplication Rules and Conditional Probability
 Multiplication rules
 Conditional probability
 Probabilities for “at least”
4.4 – Counting Rules
 The fundamental counting rule
 Factorial notation
 Permutations
 Combinations
4.5 – Probability and Counting Rules
3
Bishop Walsh School
Instruction:
2 weeks
Test:
1 day
Instruction:
3 weeks
Test:
1 day
Instruction:
2 weeks
Test:
1 day
Instruction:
3 weeks
Test:
1 day
S. Davis
SY 2015-2016
Chapter 5:
Discrete Probability Distributions
5.1 – Probability Distributions
5.2 – Mean, Variance, Standard Deviation, and Expectation
 Mean
 Variance and Standard deviation
5.3 – The Binomial Distribution
5.4 – Other types of Distributions
 Multinomial, Poisson, and Hypergeometric distributions
Chapter 6:
The Normal Distribution
6.1 – Normal Distributions
 Standard normal distribution
 Finding areas under the standard normal curve
 Normal distribution curve as a probability
6.2 – Applications of the Normal Distribution
 Finding data values given specific probabilities
 Determining normality
6.3 – The Central Limit Theorem
 Distribution of sample means
 Finite population correction factor
6.4 – The Normal Approximation to the Binomial Distribution
Chapter 7:
Confidence Intervals and Sample Size
7.1 – Confidence Intervals for the Mean when σ is Known
 Confidence intervals
 Sample size
7.2 – Confidence Intervals for the Mean when σ is Unknown
7.3 – Confidence Intervals and Sample Size for Proportions
7.4 – Confidence Intervals for Variances and Standard Deviations
Chapter 8:
Hypothesis Testing
8.1 – Steps in Hypothesis Testing
8.2 – z Test for a Mean
 P-value method for hypothesis testing
8.3 – t Test for a Mean
8.4 – z Test for a Proportion
8.5 – χ2 Test for a Variance or Standard Deviation
8.6 – Additional Topic Regarding Hypothesis Testing
 Confidence intervals and hypothesis testing
 Type II error and the power of a test
4
Bishop Walsh School
Instruction:
2-3 weeks
Test:
1 day
Instruction:
2 weeks
Test:
1 day
Instruction:
1-2 weeks
Test:
1 day
Instruction:
2 weeks
Test:
1 day

SY 2015-2016
Chapter 9 :
Testing the Difference Between Two Means, Two Proportions, and Two
Variances
9.1 – Testing the Difference Between Two Means
 Using the z test
9.2 – Testing the Difference Between Two Means of Independent Samples
 Using the t test
9.3 – Testing the Difference Between Two Means
 Dependent samples
9.4 – Testing the Difference Between Proportions
9.5 – Testing the Difference Between Two Variances
Chapter 10:
Correlation & Regression
10.1 – Scatter Plots and Correlation
10.2 – Regression
 Line of best fit
 Regression line equation
10.3 – Coefficient of Determination and Standard Error of the Estimate
 Types of variation for the regression model
 Coefficient of determination
 Standard error of the estimate
 Prediction interval
10.4 – Multiple Regression
 Multiple regression equation
 Testing the significance of R
 Adjusted R2
Chapter 11:
Other Chi-Square Tests
11.1 – Test for Goodness of Fit
 Test of normality
11.2 – Tests Using Contingency Tables
 Tests for independence
 Test for homogeneity of proportions
Chapter 14:
Sampling and Simulation
14.1 – Common Sampling Techniques
14.2 – Surveys and Questionnaire Design
14.3 – Simulation Techniques and the Monte Carlo Method
This schedule allows for up to three weeks to prepare for the AP Statistics exam.
The exam preparation includes at least three model exams with a focus on
pacing and review.
S. Davis
5
Bishop Walsh School
SY 2015-2016
AP Statistics Project:
Students will complete 2 to 3 projects during the AP Statistics course.
Example Project #1
Students will design and conduct an experiment to investigate the effects of response
bias in surveys. They may choose the topic for their surveys, but they must design
their experiment so that it can answer at least one of the following questions:




Can the wording of a question create response bias?
Do the characteristics of the interviewer create response bias?
Does anonymity change the responses to sensitive questions?
Does manipulating the answer choices change the response?
The project will be done in pairs. Students will turn in one project per pair. A written
report must be typed (singe-spaced, 12-point font) and included graphs should be done
on the computer using Excel.
Proposal: The proposal should



Describe the topic and state which type of bias is being investigated.
Describe how to obtain subjects (minimum sample size is 50).
Describe what the questions will be and how they will be asked, including how to
incorporate direct control, blocking, and randomization.
Written Report: The written report should include following sections (clearly labeled):





Title Page: in the form of a question
Methodology: Describe how the experiment was conducted and justify why the
design was effective. Note: This section should be very similar to the proposal.
Results: Present the data in both tables and graphs in such a way that
conclusions can be easily made. Make sure to label the graphs/tables clearly and
consistently.
Conclusions: What conclusions can be drawn from the experiment? Be specific.
Were any problems encountered during the project? What could be done
different if the experiment were to be repeated? What was learned from this
project?
The original proposal.
Poster: The poster should completely summarize the project, yet be simple enough to
be understood by any reader. Students should include some pictures of the data
collection in progress.
Oral Presentation: Both members will participate equally. The poster should be used as
a visual aid. Students should be prepared for questions.
S. Davis
6
Download