UNDERSTANDABLE STATISTICS Sixth Edition

Transcription

1 UNDERSTANDABLE STATISTICS Sixth Edition correlated to the Advanced Placement Statistics Standards created for Georgia McDougal Littell 5/2000

2 Advanced Placement for Georgia Subject Area: Textbook Title: Publisher: Mathematics Course: Advanced Placement Statistics Understandable Statistics, Sixth Edition 1999 Houghton Mifflin I. Exploring Data: Observing patterns and departures from patterns. Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be place on interpreting information from graphical and numerical displays and summaries. A. Interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) 1. Center and spread 2. Clusters and gaps 3. Outliers and other unusual features 4. Shapes PE: Organizing Data: Focus Problem, 22-23; Graphs, 33-45; Histograms and Frequency Distributions, 46-66; Stem-and Leaf Displays, 66-73; Review Problems, 75-80; Group Projects, 80-82; Writing Projects, 83; Using Technology, 84-87; see also topics in I.B below IAE: 22-23, B. Summarizing distributions of univariate data 1. Measuring center: median, mean PE: Measures of Central Tendency, IAE: Measuring spread: range, interquartile range, standard deviation 3. Measuring position: quartiles, percentiles, standardized scores (z-scores) PE: Measures of Variation, ; Mean and Standard Deviation of Grouped Data, , Interquartile Range, 133 IAE: , 133 PE: Percentiles, ; z Scores and Raw Scores, IAE: , Using boxplots PE: Box-and-Whisker Plots, IAE: The effect of changing units on summary measures PE: Weighted Average, , IAE: , PE: Pupil s Edition topics and pages; IAE: associated Instructor s Annotated Edition pages page 1

3 C. Comparing distributions of univariate data (dotplots, back-toback stemplots, parallel boxplots) 1. Comparing center and spread: within group, between group variation 2. Comparing clusters and gaps 3. Comparing outliers and other unusual features 4. Comparing shapes D. Exploring bivariate data PE: Mean and Standard Deviation of Grouped Data, ; Using Technology, IAE: , Analyzing patterns in scatterplots PE: Introduction to Paired Data and Scatter Diagrams, IAE: Correlation and linearity PE: Correlation and Linearity, 575, 577, ; The Linear Correlation Coefficient, , IAE: 575, 577, , , Least-squares regression line PE: Linear Regression and Least Squares, , IAE: , Residual plots, outliers, and influential points PE: Confidence Bounds for Prediction, ; Coefficient of Determination, ; Testing the Correlation Coefficient, IAE: , , Transformations to achieve linearity: logarithmic and power transformations E. Exploring categorical data: frequency tables PE: Changing Scales, 572, 575, 577, 596, 619 IAE: 572, 575, 577, 596, Marginal and joint frequencies for two-way tables PE: Histograms and Frequency Distributions, IAE: Conditional relative frequencies and association PE: Histograms and Frequency Distributions, IAE: PE: Pupil s Edition topics and pages; IAE: associated Instructor s Annotated Edition pages page 2

4 II. Planning a Study: Deciding what and how to measure Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis. A. Overview of methods of data collection 1. Census 2. Sample survey 3. Experiment 4. Observational study B. Planning and conducting surveys 1. Characteristics of a well-designed and well-conducted survey 2. Sample survey 3. Sources of bias in surveys 4. Simple random sampling 5. Stratified random sampling C. Planning and conducting experiments 1. Characteristics of a well-designed and well-conducted experiment 2. Treatments, control groups, experimental units, random assignments, and replication 3. Sources of bias and confounding, including placebo effect and blinding 4. Completely randomized design 5. Randomized block design, including matched pairs design PE: What is Statistics?, 4-19; Statistical Experiment, 161 IAE: 4-19, 161 PE: Producing Data, 9-12; Levels of Measurement, 12-16; Random Samples, 23-33; Choosing the Sample Size, IAE: 9-16, 23-33, PE: Hidden Bias, 11; Binomial Experiment, ; Control Charts, ; Experimental Design, IAE: 11, , PE: Pupil s Edition topics and pages; IAE: associated Instructor s Annotated Edition pages page 3

5 D. Generalizability of results from observational studies, experimental studies, and surveys PE: Focus Problems: Where Have All the Fireflies Gone?, 3; Say It with Pictures, 22; High Fliers: Commercial Airlines Pilot s Pay, 88; How Often Do Lie Detectors Lies?, 156; Personality Preference Types: Introvert or Extrovert?, 212; Large Auditorium Shows: How Many Will Attend?, 278; Impulse Buying, 345; The Trouble with Wood Ducks, 374; Business Opportunities and Start-Up Costs, 458; Getting the Best Price, 566; Stone Age Tools and Archaeology, 650; How Cold? Compared to What?, 740 IAE: 3, 22, 88, 156, 212, 278, 345, 374, 458, 566, 650, 740 III. Anticipating Patterns: Producing models using probability theory and simulation Probability is the tool used for anticipating what the distribution of data should look like under a given model. A. Probability as relative frequency 1. Law of large numbers concept PE: What Is Probability?, IAE: Addition rule, multiplication rule, conditional probability, and independence 3. Discrete random variables and their probability distributions, including binomial 4. Simulation of probability distributions, including binomial and geometric 5. Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable PE: Some Probability Rules Compound Events, ; Trees and Counting Techniques, ; Bayes Theorem, A1- A5 IAE: , A1-A5 PE: Introduction to Random Variables and Probability Distributions, IAE: PE: Binomial Probabilities, ; The Geometric and Poisson Probability Distributions, IAE: , PE: Additional Properties of the Binomial Distribution, IAE: PE: Pupil s Edition topics and pages; IAE: associated Instructor s Annotated Edition pages page 4

6 B. Combining independent random variables 1. Notion of independence versus dependence PE: Some Probability Rules Compound Events, IAE: Mean and standard deviation for sums and differences of independent random variables C. The normal distribution PE: Additional Properties of the Binomial Distribution, IAE: Properties of the normal distribution PE: Graphs of Normal Probability Distributions, IAE: Using tables of the normal distribution PE: Standard Units and Areas Under the Standard Normal Distribution, ; Areas of a Standard Normal Distribution, A24 IAE: , A24 3. The normal distribution as a model for measurements PE: Areas Under Any Normal Curve, ; Normal Approximation to the Binomial Distribution, IAE: D. Sampling distributions 1. Sampling distribution of a sample proportion PE: Sampling Distributions, ; Estimating µ with Large Samples, ; Estimating µ with Small Samples, IAE: , Sampling distribution of a sample mean PE: Sampling Distributions, ; Estimating p in the Binomial Distribution, IAE: , Central Limit Theorem PE: The Central Limit Theorem, IAE: PE: Pupil s Edition topics and pages; IAE: associated Instructor s Annotated Edition pages page 5

7 4. Sampling distribution of a difference between two independent sample proportions 5. Sampling distribution of a difference between two independent sample means PE: Estimating p 1 p 2, IAE: PE: Estimating µ 1 µ 2, , IAE: , Simulation of sampling distributions PE: Class Project Illustrating the Central Limit Theorem, IAE: IV. Statistical Inference: Confirming models Statistical inference guides the selection of appropriate models. A. Confidence intervals 1. The meaning of a confidence interval PE: Confidence Levels, 377, 382, IAE: 377, 382, Large sample confidence interval for a proportion PE: Confidence Interval for p, IAE: Large sample confidence interval for a mean PE: Confidence Intervals (Large Sample), , 399 IAE: , Large sample confidence interval for a difference between two proportions 5. Large sample confidence interval for a difference between two means (unpaired and paired) B. Tests of significance 1. Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power PE: Estimating p 1 p 2, IAE: PE: Estimating µ 1 µ 2, , IAE: , PE: Introduction to Hypothesis Testing, ; The P Value in Hypothesis Testing, IAE: , PE: Pupil s Edition topics and pages; IAE: associated Instructor s Annotated Edition pages page 6

8 2. Large sample test for a proportion PE: Tests Involving a Proportion, IAE: Large sample test for a mean PE: Test Involving the Mean µ (Large Samples), IAE: Large sample test for a difference between two proportions PE: Tests Involving Paired Differences, IAE: Large sample test for a difference between two means (unpaired and paired) 6. Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables) C. Special case of normally distributed data PE: Testing Differences of Means for Large, Independent Samples, IAE: PE: Chi Square: Tests of Independence, ; Chi Square: Goodness of Fit, ; Testing a Single Variance, ; Testing Two Variances, ; One-Way ANOVA, ; Two-Way ANOVA, ; Using Technology, IAE: , t-distribution PE: Estimating µ with Small Samples, ; Student s t Distribution, A25 IAE: Single sample t procedures PE: Tests Involving the Mean µ (Small Samples), IAE: Two sample (independent and matched pairs) t procedures PE: Tests Involving Paired Differences, ; Testing Difference of Means for Small Samples, IAE: Inference for the slope of least-squares regression line PE: Linear Regression and Confidence Bounds for Prediction, ; The Linear Correlation Coefficient, IAE: PE: Pupil s Edition topics and pages; IAE: associated Instructor s Annotated Edition pages page 7