Probability & Statistics, Part 2
Price: $125 | Credits: One Semester | Dept: Languages | Course ID# 226-2
Probability & Statistics, Part 2 builds on the concepts introduced in Part 1 by developing statistical inference and advanced probability models. Students evaluate sampling methods and experimental design, analyze binomial, geometric, and normal probability distributions, and use confidence intervals and hypothesis tests to draw conclusions about populations from sample data. They also investigate relationships between variables using regression and apply statistical procedures such as chi-square tests and comparisons of means and proportions. Throughout the course, students use statistical evidence to evaluate claims, make predictions, and communicate data-driven conclusions. Probability & Statistics is approved by the University of California A-G as mathematics (category C).
Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course at an accelerated rate.
Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course in an accelerated rate.
LEARNING OBJECTIVES
In this module, students gain a comprehension of the following:
- How to distinguish between populations and samples, evaluate sampling methods, identify sources of bias, and design surveys and experiments to answer statistical questions.
- How to model random phenomena using probability distributions, including binomial, geometric, and normal distributions, and apply z-scores and the Empirical Rule to calculate probabilities.
- How to use sampling distributions, the Central Limit Theorem, confidence intervals, and margin of error to estimate population parameters.
- How to formulate and evaluate statistical hypotheses, interpret p-values, recognize Type I and Type II errors, and perform hypothesis tests for proportions and means.
- How to compare groups using statistical inference, including tests for categorical and quantitative data.
- How to analyze relationships between variables using regression, interpret residuals and technology-generated statistical output, and communicate conclusions based on statistical evidence.
- How to apply statistical reasoning and inference to evaluate claims, make predictions, and solve real-world problems using data.
TOPICS COVERED
This course covers the following topics:
- Populations and Samples
- Sampling Methods
- Sources of Bias and Error
- Surveys and Experimental Design
- Observational Studies
- Random Sampling and Random Assignment
- Probability Distributions
- Binomial Distributions
- Geometric Distributions
- Normal Distributions
- Standard Scores (z-scores)
- The Empirical Rule
- Sampling Distributions
- Central Limit Theorem
- Margin of Error
- Confidence Intervals for Proportions
- Confidence Intervals for Means
- Null and Alternative Hypotheses
- Type I and Type II Errors
- Significance Levels
- p-values
- Hypothesis Tests for Proportions
- Hypothesis Tests for Means
- Statistical Conclusions in Context
- Chi-Square Tests
- Comparing Two Proportions
- Comparing Two Means
- Regression Analysis
- Interpreting Slope and Residuals
- Regression for Statistical Inference
- Interpreting Statistical Software Output
- Statistical Investigations and Communication of Results
