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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