AP Statistics Syllabus - Weebly
AP Statistics Syllabus
Primary Textbook
Daniel Yates, David Moore, Daren Starnes. The Practice of Statistics, TI - 83/89 Graphing Calculator Enhanced, 2nd Edition. New York. W.H.Freeman and Company, 2003.
Technology
All students are required to have a TI-83 Plus, TI-84, or TI-89 graphing calculator for use in class, at home, and on the AP Exam. Most concepts are initially taught without the use of the graphing calculator in order to ensure a conceptual understanding of the fundamental ideas. After a concept is thoroughly explored, students are then led through the process of using the statistical capabilities of the calculators. This is initially demonstrated by projecting the calculator skin on the smartboard as the class works through a problem. The textbook also provides step-by-step instructions for the statistical functions of these calculators.
In addition, students are exposed to statistical computer software output from various statistical packages, such as Minitab, DataDesk, and Fathom. This is done to familiarize the students with the various formats so that they can interpret the output. The interactive functions of Fathom are utilized in conjunction with the smartboard during class to demonstrate the effects of various parameter changes. Students are challenged to predict consequences of parameter changes, make the changes, and observe the actual consequences.
Course Outline
I. Planning a Study
After defining statistics, students spend the first two weeks learning how to sample and design a study. The purpose is to make the students understand that the validity of statistics rests squarely on the shoulders of good information. If the sample is not representative of the population, then all conclusions are suspect. Sampling methods and experimental design are thoroughly covered. This section is used as an introduction before continuing on to communication and interpretation of information, so that the students understand its importance.
Chapter 5: Producing Data (3 weeks)
1. Census vs. sample
2. bias in sampling
3. simple random sample
4. stratified random sample
5. cluster sample
6. systematic sample
7. observational study vs. experiment
8. designing experiments
9. control groups
10. treatments
11. blocking
12. activity- Random Rectangles - In this activity, students will utilize all four sampling methods on one set of data, and then compare the results using dotplots of the entire classes’ data. They will be required to describe the differences in the resultant distributions. This hands-on activity reinforces the distinction between the sampling methods and also introduces the students to the communications methods which are required throughout the course.
II. Exploring Data
Students are introduced to the various methods of displaying and describing both univariate and bivariate data in order to discern patterns, as well as the distinction between causation and association.
Chapter 1: Exploring Data (1 week)
13. categorical vs. quantitative data
14. displaying categorical data - pie charts, bar charts
15. displaying quantitative data - dotplots, histograms, stemplots, boxplots, ogives
(Students will create graphs manually and also with their calculators)
16. describing center - mean, median
17. describing spread - range IQR, standard deviation, outliers, variance
18. effects of linear transformations
Chapter 2: The Normal Distribution (3 weeks)
19. density curves
20. uniform distributions
21. normal distribution
22. empirical rule
23. standard normal distribution
24. z-score, using z-table
25. normal probability plot on calculator
26. normalcdf on calculator
27. invnorm on calculator
Chapter 3: Examining Relationships (3 weeks)
28. introduction to bivariate data - explanatory and response variables
29. scatterplots
30. correlation coefficient
31. coefficient of determination
32. least squares regression line
33. residual plots
34. influential points vs. outliers
35. activity - matching scatterplots and correlation coefficients (Rice University website)
Chapter 4: More on Bivariate Data (2 weeks)
36. transformations on bivariate data
37. power models and exponential models
38. marginal distributions
39. Simpson’s paradox
III. Anticipating Patterns
Chapter 6: Probability: The Study of Randomness (4 weeks)
40. definitions of probability, outcomes, and events
41. law of large numbers
42. activity -Coin tossing 50 times - graphing the outcome illustrates the law of large numbers. Students then use simulation on their calculators and compare results.
43. simulation on Fathom to demonstrate law of large numbers
44. simulation using calculators
45. probability models
46. sample space
47. conditional probability
48. independent events
49. mutually exclusive events
50. general probability rules
51. tree diagrams
Chapter 7: Random Variables (3 weeks)
52. properties of discrete random variables
53. properties of continuous random variables
54. expected value (mean) of a discrete random variable
55. normal distributions as probability distributions
56. Benford’s law
57. variance and standard deviation of a discrete random variable
58. law of small numbers
59. rules for means and variances of random variables
Chapter 8: Binomial and Geometric Distributions (2 weeks)
60. conditions for a binomial distribution
61. conditions for a geometric distribution
62. finding binomial probabilities - initially manually, and then using calculator
63. finding geometric probabilities - initially manually and then using calculator
64. binomial mean and standard deviation
65. geometric mean and standard deviation
66. normal approximation to binomial distributions
67. binomial and geometric simulations on the calculator
Chapter 9: Sampling Distributions (2 weeks)
68. definition of sampling distribution
69. unbiased statistic
70. variability of a statistic
71. sampling distributions of sample proportions
72. using the normal approximation for the sampling distribution of sample proportions - conditions
73. sampling distributions of sample means
74. means and standard deviations for sampling distributions of sample means
75. central limit theorem - activity - age of pennies
IV. Statistical Inference
Chapter 10: Introduction to Inference (3 weeks)
76. confidence intervals - creating and understanding
77. activity - Tossing coins. Students record the proportion of times a single coin lands heads up. They then construct a 95% confidence interval around their sample proportion. They then graph their confidence interval on one graph with the remainder of the class. This gives a graphical representation of the concept of what a confidence interval represents, when compared to the true population proportion of .5.
78. confidence interval for a population mean
79. calculator use for construction of confidence intervals
80. margin of error
81. tests of significance
82. null and alternative hypotheses - requirements for symbolic representation as well as verbal explanation in the context of a particular problem.
83. p-values and statistical significance
84. one-sided and two-sided tests
85. statistical significance vs. practical significance
86. type I and type II errors
87. calculating Type II error
88. power
Chapter 11: Inference for Means (3 weeks)
89. hypothesis test for a population mean (t-test)
90. t-distributions for one sample
91. checking conditions
92. standard error
93. t-distributions for difference of 2 samples; conditions
94. matched-pairs hypothesis test
95. activity - Helicopter manufacture. Students will design and test helicopters. They will need to conduct an experiment for a 2-sample t-test, a one-sample t-test, and a matched-pair t-test. The experimental design must be detailed enough so that the instructor can replicate the experiment.
Chapter 12: Inference for Proportions (2 weeks)
96. inference for a population proportion; conditions
97. confidence interval for a population proportion
98. comparing two proportions; conditions
99. confidence interval for comparing two proportions
Chapter 13: Inference for Tables: Chi-Square Procedures (2 weeks)
100. activity - M&M’s - students compare their sample’s distribution of colors to the published distribution from the company. Students perform a Chi-square goodness-of-fit test.
101. chi-square distribution
102. conditions for chi-square
103. Goodness-of-Fit
104. Homogeneity
105. Association/independence
106. use of calculator for all three tests
Chapter 14: Inference for Regression (2 weeks)
107. hypothesis test for the slope of the LSRL
108. standard error about the LSRL
109. residuals and error
110. confidence intervals for the regression slope
111. prediction intervals for regression response
Review for the AP exam/ Final exam (1 week)
112. students will take one complete AP exam (2002 exam)
113. practice on other free-response problems
114. activity - AP Murder Mystery - a comprehensive activity based on the game of Clue, which serves as a review before the final exam.
Assessments
Students will take a test for each chapter in a format which mirrors the format of the AP exam. There will be multiple choice questions followed by free-response questions. Some of the free-response questions will be actual questions from previous AP exams, others will not be. In either case, the student must demonstrate the communication skills required to explain their answers. The free-response will be graded using the same standards as are used on the actual AP exam. This is extremely important so that the students recognize the need for communication of ideas throughout the course. Additionally, there will be periodic assessments (quizzes) as needed.
This course also emphasizes the need for student interaction, and consequently there are weekly projects/worksheets which the students work on in groups for a grade. A sampling of some of the project activities has been included in this syllabus. Throughout the year, approximately 30% of the class time is spent working in groups.
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