STAT 200 Learning Objectives

STAT 200 Learning Objectives

• Variables: Explain, recognize, and provide examples of categorical and quantitative variables.
• Numerical Summaries: Interpret numerical summaries of center/location (e.g., five-number summaries) and spread (e.g., empirical rule); predict how data changes affect these summaries.
• Graphical Displays: Derive information from univariate and bivariate graphical displays (bar graphs, dot-plots, boxplots, histograms, scatterplots).
• Probabilities and Z-scores: Convert values to percentiles or z-scores for normal distributions using technology.
• Linear Regression: Identify and interpret slope, intercept, R-squared values from simple linear regression output; calculate predicted values and residuals. Interpret T-statistic and p-value for the test of slope coefficients.
• Correlation and Bivariate Plots: Match bivariate plots and descriptions to correlation coefficients; calculate correlation from R-squared and slope.
• Descriptive Statistics: Produce and interpret descriptive statistics for tabular data (conditional probabilities, risk, relative risk, odds). Include hypothesis tests for two categorical variables.
• Hypothesis Tests: Perform steps in a hypothesis test of association of two categorical variables from contingency table data; formulate hypotheses, calculate expected counts, find the chi-square statistic, calculate p-value, and interpret results.
• Population vs. Sample: Recognize the difference between population and sample, and between parameter and statistic.
• Sample Size and Standard Error: For large populations, understand that precision of estimation is a function of sample size. Recognize the inverse square root relationship between sample size and standard error.
• Study Types: Recognize randomized experiment vs. observational study and explain implications for causation; define simple random sampling.
• Variables in Studies: Explain, recognize, and cite examples of explanatory, response, and confounding (lurking) variables.
• Confidence Intervals: Recognize the similarity among confidence intervals; exploit this similarity to derive intervals for common population quantities (proportions and means).
• Confidence Interval Details: Give correct informal and formal explanations of confidence intervals; explain how factors like sample size, confidence level, and standard error affect the interval's width.
• Hypothesis Formulation: Correctly construct null and alternative hypotheses about population quantities in real-life situations.
• Test Statistics and P-values: Recognize similarity among test statistics of the standardized score variety (e.g., proportions, means); calculate p-values, define p-value correctly, and interpret p-values and confidence intervals for decision-making.
• Inference Situations: Recognize and distinguish among common inference situations (one mean/proportion, difference of two means/proportions, paired means), apply and interpret confidence intervals and tests in these situations.
• Bootstrap Distributions: Explain how to generate and use a bootstrap distribution to create confidence intervals for means, differences in means, proportions, and differences in proportions; use both formula (statistic ± 2xSE) and percentiles.
• Randomization Distributions: Describe the process of creating a randomization distribution for a given sample and null hypothesis; use technology to calculate p-value, connecting it to the motivation behind a randomization distribution.