Segment 1
• Dotplots, stemplots (back-to-back stemplots), histograms, cumulative frequency plots, and parallel boxplots • Center, shape, spread, clusters, gaps, outliers and other unusual features • Position using quartiles, percentiles, and standardized (z) scores • Boxplots (and modified) with the five number summary • Center and spread both within a group and between groups • Position of different distributions using standardization • Correlation and linearity • Least-squares regression lines • Transformations to achieve linearity (logarithmic and power) • Marginal and joint frequencies for two-way tables • Conditional relative frequencies and determine association • Distributions in bar charts and residual plots • Populations, samples, and random selection • Sources of bias in sampling and surveys (undercoverage, voluntary response, including confounding variables, the placebo effect, and blinding) • Sampling methods (simple random sampling, stratified random sampling, and cluster sampling) • Treatments, control groups, experimental units, random assignments, and replication • Completely randomized designs • Different experimental designs (randomized block design, matched pairs design) • Generalize results from collected data • Probability models • Long-run relative frequencies • Law of Large Numbers • Independence and disjoint • Conditional probability • Mean and standard deviation for sums and differences of independent random variables • Binomial and Geometrical distribution, finding the mean and standard deviation • Properties of the normal distribution as a model for measurements • Sampling distribution of a sample proportion and sample mean • Central Limit Theorem • Sampling distribution of a difference between two sample proportions and means
Segment Two
• Conduct significance tests • Probabilities in Type I, Type II errors, and Power • Confidence intervals and significance tests of means (both 1 sample and 2 sample) • Sample size for a desired margin of error • Confidence intervals and significance tests of proportions (both 1 sample and 2 sample) • Determine sample size for a desired margin of error • Chi-squared goodness of fit and chi-squared test of independence • Assumptions for inference for regression or a linear regression test • Conduct significance tests for linear regressions • Useful language for symbolically modeling and thus simplifying and analyzing our world • Mathematics is a logical and objective means of analyzing and solving problems • Effective communication of mathematics is essential to its application • Analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns • Data must be collected according to a well-developed plan if valid information is to be obtained • Probability is the tool used for anticipating what the distribution of data should look like under a given model • Statistical inference guides decision making
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