STT 215: Core Concepts and Learning Outcomes in Introductory Statistics

Student Learning Outcomes

Overview

This section outlines the essential skills and knowledge students are expected to acquire upon completing STT 215, an introductory statistics course. The outcomes emphasize understanding data variability, probability, inferential methods, and the use of technology in statistical analysis.

• Describing Variability: Students should be able to describe the variability inherent in univariate (single variable) and bivariate (two variables) data using numerical summaries, graphical representations, and written explanations.

• Role of Randomization: Students should explain how randomization is used in designed experiments and standard sampling methods to reduce bias and ensure representative samples.

• Probability Computation and Interpretation: Students should compute and interpret probabilities for everyday random phenomena and common sampling distributions.

• Confidence Intervals: Students should compute and interpret confidence intervals for one- and two-sample cases, providing a range of plausible values for population parameters.

• Hypothesis Testing: Students should construct and interpret hypothesis tests for one- and two-sample cases, as well as for two-way tables, utilizing p-values to draw conclusions.

• Use of Technology: Students should be able to use statistical software or calculators to perform analyses and simulations, except for the simplest calculations.

Course Content

Core Topics

The following chapters represent the foundational topics covered in the course. Mastery of these areas is essential for understanding the principles and applications of statistics.

• Chapter 1: Data Collection

  • Methods for gathering data, including surveys, experiments, and observational studies.

  • Understanding sampling techniques and sources of bias.

• Chapter 2: Organizing and Summarizing Data

  • Constructing tables and graphs (e.g., frequency tables, histograms, bar charts).

  • Summarizing data distributions visually and numerically.

• Chapter 3: Numerically Summarizing Data

  • Measures of central tendency (mean, median, mode).

  • Measures of variability (range, variance, standard deviation).

• Chapter 4: Describing the Relation between Two Variables

  • Scatterplots, correlation, and regression analysis.

  • Identifying and interpreting relationships between variables.

• Chapter 5: Probability

  • Basic probability rules and concepts.

  • Calculating probabilities of events.

• Chapter 6: Discrete Probability Distributions

  • Probability mass functions (PMFs) for discrete random variables.

  • Common distributions such as the binomial and Poisson.

• Chapter 7: The Normal Probability Distribution

  • Properties of the normal distribution.

  • Standardization and the use of z-scores.

• Chapter 8: Sampling Distributions

  • Distribution of sample statistics (e.g., sample mean).

  • Central Limit Theorem.

• Chapter 9: Estimating the Value of a Parameter

  • Point estimation and interval estimation.

  • Constructing and interpreting confidence intervals.

• Chapter 10: Hypothesis Tests Regarding a Parameter

  • Formulating null and alternative hypotheses.

  • Calculating test statistics and p-values.

  • Making decisions based on statistical evidence.

• Chapter 11: Inference on Two Population Parameters

  • Comparing means and proportions from two populations.

  • Constructing confidence intervals and hypothesis tests for differences.

Additional info:

• Students are encouraged to use statistical technology for data analysis and simulation.

• Some instructors may cover additional topics beyond the core chapters.