Prerequisite Skills & Common Themes of AP Stat Qs 1.Interpreting the question in Probability Notation 2.Recognizing that a situation a.demands a Hypothesis Test / Confidence Interval b.employs the Central Limit Theorem c.deals with a Normal / Binomial / Geometric distribution d.suggests the Slope / Y-intercept / R2 pertaining to the LSRL 3.Interpreting the question accurately and attaching relevant symbols to the given numbers 4.Generalizing the conclusions of a study [experiment / survey] 5.Constructing & Interpreting parallel Boxplots and back-to-back Stemplots 6.Verifying Assumptions of a Binomial / Geometric Distribution 7.Setting up a pair of Hypothesis in Words / Symbols 8.Calculating / Interpreting Z-scores 9.Determining degrees of freedom and Critical Value for a.a 2-sample t-test OR for the Confidence Interval, b.Matched-Pairs t-test OR for the Confidence Interval, c.Chi Square Test of Goodness of Fit, d.Chi Square Test of Independence / Chi Square Test of Homogeneity of Proportions, e.t-test for Regression [slope of the LSRL] OR for the Confidence Interval 10.Calculating probability for a Normal Distribution, and value corresponding to a percentile 11.Estimating r from a scatterplot 12.Identifying sources of Bias in Sample Designs / Eliminating Bias 13.Identifying Type I and Type II Errors, and how to reduce them 14.Calculating Summary Statistics [Mean, Median, Percentile, Range, IQR, Standard deviation, Variance] for Linear Transformed Variables [Y = a + bX] 15.Determining Quartiles from a Plot [Histogram / Stemplot / Boxplot] 16.Interpreting Confidence Intervals / Margin of Error 17.Calculating the Mean and Standard Deviation for the Sum of 2 or more Random Variables, given their distributions [~ Normal, Binomial, Probability Distribution Table] 18.Identifying the relevant Test of Hypothesis for a situation described 19.Calculating the probability of an outcome for a Binomial Distribution and calculating the Expected Value & Standard Deviation; likewise for a Geometric Distribution 20.Calculating the Outlier Limits for Symmetric & Skewed Distributions 21.Identifying factors affecting the Margin of Error / Width of Confidence Intervals [Reducing / Increasing] 22.Calculating the Mean, Standard Deviation, Percentiles and IQR of a random variable expressed in various formats: a.Probability Distribution Table b.Frequency Distribution Table

c.Histogram d. Stemplot 23.Recognizing that a Probability Distribution table with X and P(X) immediately yields the Average / Expected Value / Mean of the random variable 24.Calculating [Conditional] Probabilities by first making a Probability Table 25.Calculating the Mean and Standard Deviation of the Sampling Distribution of Sample Proportion / Sample Mean 26.Calculating the Minimum Sample Size for a given Margin of Error 27.Using Conditional Probability formula: P(A | B) = P(A and B) / P(B) and back-solving: a.P(A and B) = P(A | B) ⋅ P(B) b.P(A and B) = P(B | A) ⋅ P(A) 28.Calculating the Standard Error (S.E.), Margin of Error (M.E.), and Confidence Intervals (C.I.) for various Estimates / Parameters a.Means, b.Proportions, c.Difference of Means, d.Difference of proportions, e.Mean Differences f.Slope of the LSRL 29.Calculating the Expected Frequency for a Chi-Square table 30.Interpreting a scatterplot in terms of Form, Association and Strength [applying the y = x line for paired data] 31.Understanding the Effect on sample Size on Standard Error and Margin of Error 32.Identifying the components of an experiment: Explanatory & Response variables, the Treatments, Confounding variables, Placebo effect, single- and double-blind experiments. 33.Identifying the role [why?] and implementation [how?] of key aspects of experiments: Randomization, Control Group, Replication, [Direct Control, Blocking] 34.Identifying relevance of using Mean and Standard Deviation over Median and IQR [/ vice versa] to describe distributions 35.Identifying the cell that “contributes” the most to the χ2 Value [(O – E)2/E is largest!] 36.Distinguishing the Chi Square Test of Goodness of Fit, Test of Independence and Test of Homogeneity of Proportions in terms of Hypotheses and Conditions 37.Applying the Central Limit Theorem for Means / Proportions 38.Evaluating if Conditions have been satisfied for perform a Test of Significance [Hypothesis Test / Confidence Interval] 39.Performing Hypothesis Tests on a calculator and drawing inferences 40.Calculating Confidence Intervals on a calculator and drawing inferences 41.Identifying properties of the t-distribution & χ2-distribution curves 42.Recognizing when to employ the t-test over the z-test

43.Distinguishing an experiment from an observation study / survey 44.Estimating the Mean and Standard Deviation from a Normal Curve using the Range ~ 6σ relationship 45.Recognizing the effect of Extreme Observations / Outliers on the Summary Statistics [Mean, Median, Percentile, Range, IQR, Standard deviation, Variance] 46.Recognize, for a Binomial Distribution, the relationship of probability of Success, P, and the shape of the distribution; that the modal value ~ E(X) 47.Comparing 2 distributions using Z-scores / Percentiles 48.Distinguish Matched Pairs vs. 2-Sample t-test for Difference of Means 49.Distinguishing various Sampling Designs a.Census b.Simple Random Sample c.Stratified Random Sample d.Systematic Sample e.Cluster Sample f.Multi-Stage Sample 50.Proving Independence using Probability Rules, Segmented Bar Graphs, Probability Tables & Chi-Square Test of Independence 51.Recognizing that Probabilities, Expected Values, the results of Tests of Significance relate to long-run outcomes 52.Distinguishing Exponential (y = A⋅ Bx) and Power (y = A⋅ xB) transformations 53.Knowing Properties of Z-scores 54.Interpreting Correlation Coefficient, Coefficient of Determination, Slope, Y-Intercept, Residual, Standard Error of the Slope (SE(b), Standard Error of the Residuals (s) 55.Understanding the relationship between the Correlation Coefficient, Slope and Coefficient of Determination 56.Interpreting computer printouts a.Regression Analysis: identifying slope, y-intercept, R2, s, SE(b), P-value for Ho: ® = 0 b.Hypothesis Tests & Confidence Intervals 57.Calculating P(at least one “Success”) 58.Recognizing that Matched Pairs [1-sample t-test for dependent samples] yields a lower Standard Error, [S.E.(X1-2)] over Randomized Block Designs with 2 Treatments [ 2-sample t-test for independent samples] [S.E.(X1 – X2)], thereby resulting in a higher test-statistic, t* => lower P-value…Differences are likelier to be statistically significant 59.Deriving the shape of a distribution from an Ogive, via the 5-Number Summary / Boxplot 60.Identify Influential Points 61.Recognizing the relative positions of Mean, Median and Mode for Skewed distributions 62.Distinguishing Z-scores and the Z~ N(0, 1) distribution 63.Applying the 68-95-99.7% Empirical Rule for Normal distributions

64.Recognizing various methods & notations to calculate Binomial probabilities, including Normal Approximations using x or p as the estimate 65.Describing the Appropriateness of a Regression Model using a computer printout & residual plot 66.Distinguishing Outliers, Influential Points and Residuals 67.Recognizing that Confidence Intervals yield interval estimates for the Parameter of Interest based on the Statistic, while Hypothesis Tests test the claim that the Parameter assumes a certain value 68.Distinguishing Mutually Exclusive and Independent Events, and the relationship between them 69.Recognizing the rationale for each of the Assumptions for Inference [Randomization, Independence and Normality] 70.Creating a Probability Distribution Table via listing Outcomes, P(each Outcome) and Value taken by the random variable, x 71.Applying the Central Limit Theorem 72.Calculating test statistics a.t-score for Means / Difference of Means / Mean Differences / slope of the LSRL b.Z-score for Proportions / Difference in Proportions c.χ2 Value 73.Calculating P-values, given sample size and test-statistic, for 1-tailed and 2-tailed tests 74.Recognizing that Estimates are Pooled only for Tests of Hypothesis for Difference in Proportions 75.Identifying Type I and Type II Errors, and ways to reduce them 76.Calculating Power of Test, and recognizing ways to increase Power 77.Understanding that one value (Mean or Proportion) being higher / lower than another does not imply a (Statistically) Significant Difference; that Tests of Significance [Hypothesis Tests / Confidence Intervals] alone reveal such differences 78.Recognizing that Random Sampling procedures always yield Unbiased estimates; that SRS yields estimates with the lowest variability 79.Identifying the factors affecting the value of the Test-statistic 80.Distinguishing the role of Randomization in Observation Studies vs. Experiments 81.Performing non-standard Tests of Hypothesis [e.g. H0: µ 1 - µ 2 = 10; H0: P1 - P2 = 2%; H0: β = 1] 82.Applying the general P(A or B) Rule 83.Recognizing the relationship between Confidence Level and Significance Level 84.Identifying the Assumptions for a test of Significance for regression, using Residuals 85.Recognizing that if 2 factors are Independent [using the Chi-Square Test], the Proportions shall also be Homogenous

AP Exam Review: Common Themes of AP Qs

Most critical concepts and skills assessed on the AP Exam