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AP/ACC-Statistics Course Outline Chaminade College Preparatory School course: AP/ACC-Statistics (STA 470) Advanced Credit Program through the University of Missouri – St. Louis course: MATH 1310 Elementary Statistical Methods Course Outline: UNIT I: EXPLORING AND UNDERSTANDING DATA (15 BLOCKS) Section A Data (Chapter 2) 3 Blocks Who, what, when, where, why (and sometimes how). Section B Categorical and quantitative variables Quiz Displaying and Describing Categorical Data (Chapter 3) 3 Blocks Frequency and relative frequency tables The area principle Bar charts, pie charts Computer output: keys to observe in bar charts and pie charts generated by computer packages Contingency tables and conditional distributions Section C Simpson’s paradox Quiz Displaying and Summarizing Quantitative Data (Chapter 4) 3 Blocks Histograms, relative frequency histograms, stem-and-leaf displays, and dotplots Interpreting quantitative data: communicating the shape, center, and spread of the distribution Quartiles, IQR, and outliers 5-number summary, mean, variance, and standard deviation Calculator application: Inputting a list of values, draw histograms, calculate 5number summary, mean, and standard deviation Quiz Computer output: keys to observe in displaying and summarizing quantitative variables by computer packages Section D Understanding and Comparing Distributions (Chapter 5) 2 Blocks Boxplots, 5-number summaries, and outliers Interpreting distributions of groups by comparing groups with histograms and boxplots Calculator application: Draw histograms and boxplots , aid in determining outliers Quiz Computer output: comparing distributions generated by computer packages Section E The Standard Deviation as a Ruler and the Normal Model Standardizing of values, z-scores, and normal distribution 4 Blocks Shifting and rescaling data 68-95-99.7 Rule Normal percentiles and area under the curve Using z-tables, and calculator statistics functions Assessing normality and normal probability plots Calculator application: z-score to area under the curve, area less than a value back to a z-score, and drawing normal probability plots Interpreting the difference between raw score, standardized score, area under the curve, and percent of coverage of under the curve Unit I Test UNIT II: EXPLORING RELATIONSHIPS BETWEEN VARIABLES (5 BLOCKS) Section A Scatterplots, Associations, and Correlation 2 Blocks Scatterplots (describing pattern, form, direction, strength, and outliers) Response and explanatory variables Correlation Section B Calculator application: Drawing scatterplots, and computation of means and correlation of variables Quiz Linear Regression 3 Blocks The least squares regression line Predicted values and residuals Correlation, standard deviation, and regression slope Means of x and y, and regression intercept Interpreting the value 𝑅2 - the variation accounted for by the explanatory variable Calculator application: interpretation of least square regression line, and the explanation of the variation of the response variable by the explanatory variable Unit II Test Computer output: keys to interpretation of regression table of results made by statistical packages UNIT III: GATHERING DATA (4 BLOCKS) Section A Understanding Randomness 2 Blocks Simulations Random numbers Calculator application: Use of lists, random integer generators, and data displays Project: emphasis on developing the components, objectives, and analysis of a simulation. Class divided into groups, each taking either “The Spread of a Rumor”, “The Duck Hunters”, “Airline Overbooking”, or “The Spread of an Epidemic” project. Students will: (a) develop the individual component to be randomly generated (b) define the trial to be simulated by the components Quiz (c) define the response variable to be recorded (d) perform an analysis of multiple trials (e) interpret the results in order to present any conclusions that can be drawn from the simulation. Section B Sample Surveys 2 Blocks Examine a part of the whole, bias Randomize Sample size, census, population, parameters, statistics Simple random samples (SRS) Unit III Test UNIT IV: RANDOMNESS AND PROBABILITY (8 BLOCKS) Section A From Randomness to Probability 3 Blocks Trials, outcomes, events, and sample spaces Law of large numbers Modeling probability, personal probability, and formal probability Complement rule, addition rule, and multiplication rule Fundamental theorem of statistics Assumptions and conditions Sampling distribution model for the mean Section B Mean and standard deviation Quiz Probability Rules! 2 Blocks The General Addition Rule Conditional Probability from a contingency table The General Multiplication Rule Independence Drawing without Replacement Section C Tree Diagrams Quiz Random Variables 1 Block Interpreting the expected value as an estimate of the center of a probability distribution Section D Interpreting the variance as an estimate of the spread of a probability distribution Quiz Probability Models 2 Blocks Geometric probability model for Bernoulli Trials Independence Binomial probability model for Bernoulli Trials Identifying the model used for a particular situation Normal Model used to approximate a binomial model Unit IV Test Calculator application: Factorials, combinations, geometric distribution, binomial distribution, and approximations using Normal distribution UNIT V: CONFIDENCE INTERVALS AND HYPOTHESIS TESTING (7 BLOCKS) Section A Confidence Intervals for Proportions 2 Blocks Observed proportion and standard error Meaning of confidence intervals One-proportion z-interval Margin of error, critical values Assumptions and conditions necessary for interpreting confidence interval Choosing sample size Calculator application: Calculation of one-proportion z-interval Section B Testing Hypotheses About Proportions Quiz 1 Block Hypotheses Standard deviation and standard error P-value and hypothesis testing Two-sided and one-sided hypothesis Section C Calculator application: One and Two-sided hypothesis testing using one-proportion z-test Quiz Tests, Errors, and the Power of the Test 2 Blocks Null hypothesis Alpha levels, statistical significance Confidence intervals and hypothesis tests Type I and Type II errors Power Selecting the alternative hypothesis to reduce the Type I and Type II errors Calculator application: One-sample z-interval and one-sample z-test Quiz Project: using Minitab to conduct an inference study on one sample from a population with known standard deviation Section D Comparing Two Proportions 2 Blocks Variance of sum/difference of random variables Standard deviation of the difference between two proportions Assumptions and conditions necessary for interpreting the difference between two proportion Sampling distribution for two proportions Two-proportion z-interval Standard error of the difference Pooled two-proportion z-test Unit V Test Calculator application: Two-proportion z-interval, two-proportion z-test, and the concept of pooling FIRST SEMESTER EXAM UNIT VI: LEARNING ABOUT THE WORLD (12 BLOCKS) Section A Inference About Means 3 Blocks Central limit theorem Standard deviation of the mean Gosset’s t-model Confidence interval for the mean, one-sample t-interval Assumptions and conditions necessary for t-model being used Standard error of the mean, degrees of freedom One-sample t-test Margin of error, and sample size Calculator application: One-sample t-interval and one-sample t-test Quiz Project: Minitab project based on illustrating the Central Limit Theorem, emphasizing comparisons of descriptive statistics, means, and medians. Section B Comparing Means 3 Blocks Standard deviation of the difference of means Standard error of the difference of means Two-sample t-interval Degrees of freedom formula Assumptions and conditions necessary for two-sample t-model being used Alternative degrees of freedom Pooled t-test 𝑠𝑝𝑜𝑜𝑙𝑒𝑑 Standard error for pooled difference of means Confidence interval for pooled difference of means Hypothesis testing for pooled difference of means Calculator application: Two-sample t-interval, pooled t-test, and the aggression computation of the degrees of freedom, confidence interval /hypothesis test with pooled difference of means Quiz Computer output: study the method of displaying the results of a two-sample method in a statistical package Section C Paired Samples and Blocks Paired data, blocking, and matching Paired t-test Assumptions and conditions 2 Blocks Confidence intervals for matched pairs Effect size and blocking Section D Computer output: interpretation of different statistical packages display of a matched pairs and paired t analyses Quiz Comparing Counts 1 Block Goodness-of-Fit Assumptions and conditions Chi-square calculations Chi-square test of homogeneity Assumptions and conditions Examining the residuals Section E Calculator application: Chi-square goodness of fit testing, and Chi-square test of homogeneity Quiz Inference for Regressions 3 Blocks Population and sample, parameters and statistics Idealized line and fitted line Assumptions and conditions Residuals Spread around the line, spread of the x’s, and sample size Standard error for the slope Sampling distribution for regression slopes Hypothesis tests and confidence intervals Confidence interval for the predicted mean value of 𝑥𝑦 Prediction interval for an individual with that x-value Calculator application: hypothesis testing for slope and regression, and confidence intervals for predicted mean and individual x-value Unit VI Test Computer output: statistical summary and regression analysis output from different statistical package UNIT VII: REVISITING EARLIER TOPICS (20 BLOCKS, GROUP-FOCUSED INSTRUCTION) Section A Re-expressing to equalize spread across groups 1 Block Alleviating the problem of comparing groups by transforming data using different mathematical functions Section B Section C Normal Probability Plots 1 Block Using the normal probability plot along with histograms to judge whether a Normal Model may be appropriate Quiz Applications of Correlations and Scatterplots 1 Block Correlation tables Straightening scatterplots Section D Investigating Linear Regressions 2 Block Residuals used to investigate patterns Residual standard deviation Regression assumptions and conditions necessary for appropriate predictions Analyzing two regressions Calculator application: Display of residual plots Section E Regression Wisdom Test 2 Blocks Regression analysis Extrapolation Outliers, leverage, and influence Lurking variables and causation Section F Computer output: working with summary values generated from statistical packages Quiz Re-expressing Data to Get the Regression Straight 2 Blocks Goals of re-expression Ladder of Power Exponential, Logarithmic, and Power functions Section G Calculator application: Calculator short-cut regressions for Quadratic, Cubic, Quartic, Natural Logarithmic, Exponential, Power, and Logistic regressions Quiz Sample Surveys 2 Blocks Stratified random sampling Cluster and multistage sampling Systematic samples Defining the actual population to clarify the variables to be studied Section H Valid surveys Quiz Experiments and Observational Studies 4 Blocks Observational studies, prospective studies Random assignment Factors, response variables, levels, and treatments Subjects (participants) and experimental units Control, randomize, replicate, and block Diagrams Sample surveys vs. experiments Control treatments, blinding, and placebos Random block design Matching Confounding Section I Project: small group problem as students design and administrate a survey on a topic of their choice. The students will collect and analyze data using descriptive and inferential statistics, drawing conclusions from their analysis. Test Probability Rules 1 Block Reversing the conditions of conditional probability Section J Bayes’s Rule Quiz Sampling Distribution Models 1 Block Simulating the sampling distribution of a mean Section K Tests and Intervals 1 Block A 95% confidence interval for small samples Power Reducing Type I and II errors Section L Section M Computer output: examining different statistical packages representation of hypothesis tests Quiz Comparing Two Proportions 1 Block Null hypothesis means no difference Quiz Inferences About Means 1 Block Background behind degrees of freedom Computer output: investigate statistical packages examination of inference for means Test Final exam will precede the AP test and will emphasize the format used on the AP exam. AP material will be used to emphasize the topics in that context.