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MRS. CONWAY, AP STATISTICS FINAL EXAM STUDY GUIDE SENIOR FINAL EXAM The final exam will be comprised of multiple choice questions and short answer questions. The format of your final will be the same format as all of your previous tests and your midterm. You will be able to use the same formula sheet that is provided on the AP Statistics exam. The best way to review for your test is to review problems from your old tests. Many questions on your final will be similar to questions from your old tests. The material from the second semester will be approximately two thirds of the exam and the material from the first semester will be approximately one third of the exam. Since inference will be one of the most prevalent topics on the exam (it was covered in Chapter 10 through 14 of your textbook and was the material we covered almost all of second semester), I am attaching a document with twelve additional practice problems on inference. The answers to these review questions are also posted. You can expect that there will be problems that are similar to these review problems on your test. Below, I’ve included the list of topics that we have covered this year and well as the corresponding textbook chapters. AP Statistics topics covered during the 2010 -2011 school year: Unit 1: Exploring Data, YMS Chapter 1 Graphing and Numerical Distributions Identify variables as categorical or quantitative Construct and interpret graphical displays of univariate data: dotplots, stemplots, pie charts, histograms, bar charts, ogives, box-and-whisker plots, and cumulative frequency charts Describe distributions using shape, center, spread and outliers Summarize distributions with relative location and position Look for overall skewness and patterns in a distribution Give appropriate numerical measures of central tendency and dispersion Compare distributions graphically Use TI graphing calculator to obtain summary statistics including the 5 number summary Use TI graphing calculator to create charts and box-whisker-plots Unit 2: The Normal Distribution, YMS Chapter 2 Density Curves and the Normal Distribution; Standard Normal Calculations Compute and interpret the standardized value (z-score) of a data point Calculate the proportion of values above, below, or between a stated number(s) given a stated mean, standard deviation, and normal distribution Understand the relationship between area under a curve and proportion Identify mean and median on a density curve Know the properties of standard deviation and the effects of changing the unit of measurement Understand changes to the mean, standard deviation and variance of a data set when all data within the set is increased or decreased by a number and/or multiplying by a number Understand and apply the Empirical Rule and know why it is different from Chebychev’s Rule Determine if a distribution is normal Use TI graphing calculator to find the area under the normal curve MRS. CONWAY, AP STATISTICS FINAL EXAM STUDY GUIDE Unit 3: Probability, YMS Chapter 6 Understand and apply rules of probability, including the addition and multiplication rules Determine if two events are disjoint, complementary or independent Determine unions and intersections of events Create and interpret Venn diagrams and tree diagrams Apply counting techniques in solving probability problems Understand the difference between mutually exclusive and independent Construct and interpret sample spaces for random events Calculate probabilities for combinations of events Understand and compute conditional probabilities Unit 4: Random Variables, YMS Chapter 7 Discrete and Continuous Random Variables, Means, and Variances of Random Variables Define random variable, discrete random variable, and continuous random variable Identify and describe discrete and continuous data and variables Compute probabilities of normal random variables Compute probability distributions of discrete random variables and continuous random variables Calculate mean and standard deviation for sums and differences of two independent random variables Calculate and interpret expected value of a random variable Use law of large numbers to approximate the mean of a distribution Use graphing calculator to estimate probabilities using simulation Unit 5: Production of Data, YMS Chapter 5 Understand, identify and describe methods of Data Collection – census, surveys, study, experiment Plan and conduct surveys – populations, samples, bias, sampling methods (simple random, stratified, systematic, cluster, multi-stage, voluntary response) Identify when sampling bias occurs and identify the type of sampling bias Plan and conduct experiments – 3 principles (control, randomization, replication), bias (placebo effect, Hawthorne effect, confounding variables, blinding), randomization, blocks, and matched pairs Identify the factors of an experiment, explanatory variables, treatments, response variables, and experimental units or subjects of an experiment Recognize the placebo effect and when double-blinding should be used Understand and apply randomization when assigning subjects to groups or to complete a simple random sample Understand the difference between surveys and experiments and be able to determine given scenarios Determine if/why an experiment or survey may be flawed Generalize results to population MRS. CONWAY, AP STATISTICS FINAL EXAM STUDY GUIDE Unit 6: Binomial and Geometric Distributions, YMS Chapter 8 Binomial Distributions and Geometric Distributions Verify conditions of a binomial distribution, verify conditions of a geometric distribution Understand when it is appropriate to use a binomial distribution vs. a geometric distribution Compute cumulative distribution functions, cumulative frequency distribution tables, cumulative frequency histograms for binomial and geometric random variables Calculate means and standard deviations of binomial random variables and geometric random variables Compute probabilities using a normal approximation to the binomial distribution Use TI graphing calculator to compute binomial and geometric probabilities Unit 7: Examining Relationships, YMS Chapter 3 Scatter Plots, Correlation, Least-Squares Regression Classify variables as quantitative or categorical Assess a relationship between two variables by creating and analyzing scatter plots Compute and be able to describe the meaning of the least squares regression line Compute and interpret the correlation coefficient, the coefficient of determination, the slope and the y-intercept Construct and interpret a scatterplot and regression line, and the quality of a regression line for bivariate data Compute and understand residual values and use TI calculators to display residual plots Use TI calculators to display scatterplots and superimpose lines of best fit Use Microsoft Excel to display scatterplots and superimpose lines of best fit Unit 8: Two-Variable Data, YMS Chapter 4 Use logarithmic and power transformations to achieve linearity Determine when a transformation might be necessary to achieve linearity Identify exponential growth and decay Understand when to use caution in regression and correlation due to extrapolation, confounding and lurking variables Understand and be able to explain the difference between correlation and causality and what gives the best evidence for causation Explain the criteria for establishing causation when experimentation is not possible Be able to recognize and explain the parts of a two-way table Use a two-way table to compute marginal distributions Recognize and be able to give an example of Simpson’s paradox Use TI calculators and Microsoft Excel to complete transformations to achieve linearity Unit 9: Sampling Distributions, YMS Chapter 9 Understand the difference between parameters and statistics and be able to define these in a sample Understand and describe the difference between bias and variability and how to influence each Recognize when a problem involves a sample proportion or the mean of a sample Compute and interpret mean and standard deviation of a sampling distribution Understand the relationship between standard deviation and sample size Describe the shape, center and spread of a sample proportion Use a normal approximation to solve probability problems for sample proportions and for sample means State, understand, and apply the central limit theorem MRS. CONWAY, AP STATISTICS FINAL EXAM STUDY GUIDE Unit 10: Introduction to Inference, YMS Chapter 10 Describe statistical inference and the basic form of all confidence intervals Construct and interpret a confidence interval for the mean of a normal population with known standard deviation Define null and alternative hypothesis for a testing situation for a population mean Use a TI graphing calculator to calculate the 1-sample z statistic and P-value about the mean for 1sided and 2-sided tests Describe margin of error and how to control margin of error Compare values to assess statistical significance and analyze the results of significance tests Define Type I errors and Type II errors and explain power in significance testing Define and interpret standard error in relation to and Unit 11: Inference for Distributions, Means and Proportions, YMS Chapter 11 and 12 Understand when to use inference about a mean and when to use the comparison of two means Compute and analyze a one-sample t test to hypothesize a population mean and understand any problems that may be present with the test Compute and analyze a two-sample t test to compare the difference between two means and understand any problems that may be present with the test Use the TI graphing calculator to calculate confidence intervals for difference between two means Use the TI graphing calculator to test hypothesis Understand when to use one-sample, matched pairs, or two-sample procedures Use z procedure to get confidence interval for population proportion Complete one-sample and paired data t significance tests Complete a significance test for a population proportion Complete two-sample z procedure to test the hypothesis for equality of proportions in two populations Use the TI graphing calculator to calculate confidence intervals Use the TI graphing calculator to test hypothesis Unit 12: Inference for Tables and Inference for Regression, YMS Chapter 13 and 14 Understand and complete tests for goodness of fit and inference for two-way tables Complete the appropriate chi-squared procedure and calculate the various relevant components depending on the given situation Construct a confidence interval for the difference between two population means and two population proportions Complete the significance test for the difference between two population means and two population proportions Recognize when to use linear regression inference for a set of data Interpret the regression for a given set of data Interpret chi-squared results and regression results from a computer printout