
Course Overview
Course Goals
Semester B of Probability and Statistics is designed to give 11th- and 12th-grade students a more in-depth look at statistics and its many applications, with an emphasis on inferential statistics. Students are also introduced to advanced counting techniques as well as probability and its applications.
The semester begins with the concept of sample space, basic probability, and the difference between theoretical and experimental probabilities. A more in-depth look at probability follows, with an emphasis on compound and conditional probabilities.
Students explore normal data distributions and its properties, followed by a look at the standard normal distributions and its usefulness as a probability model for making inferences about a population. The remainder of the semester is devoted to hypothesis testing using various significance tests such as 1- and 2-sample z-tests, 1- and 2-sample t-tests, significance tests involving proportions, and chi-square goodness of fit tests. Hypothesis testing is then put into practice through a variety of real-world of applications and projects.
Each of the five units in Semester B includes twelve lessons and one project. Each lesson has a minimum of thirteen formative assessment questions to enable students and their teacher to gauge student understanding. Summative assessments include three quizzes in each unit, a test for each unit, and a semester exam covering all five units. Each project uses concepts covered in the unit.
- Unit 1: Determine theoretical and experimental probabilities using probability rules, and determine if two events are independent.
- Unit 2: Identify mutually exclusive and non-mutually exclusive events, determine binomial probabilities, and calculate expected value.
- Unit 3: Use permutations and combinations to calculate probabilities, and apply the properties of normally distributed data.
- Unit 4: Understand the central limit theorem, determine confidence intervals, and use hypothesis testing to compare proportions and means, and to determine the relationship between categorical variables.
- Unit 5: Distinguish between parametric and non-parametric statistics and apply these concepts to examine topics including health science and market research.
Curriculum Content and Skills Focus
Unit 1: Introduction to Probability
- Objective 1: Identify the sample and population in a research setting.
- Objective 2: Use the probability continuum to estimate probabilities ranging from impossible to certain events.
- Objective 3: Differentiate between theoretical and experimental probabilities and calculate probabilities for each.
- Objective 3: Identify independent events and calculate probabilities involving independent events.
- Objective 4: Identify events as mutually exclusive and calculate probabilities involving mutually exclusive events.
- Objective 5: Calculate probabilities for conditional events.
- Objective 6: Design a study that involves the conditional probability of an event A given that event B has occurred.
Unit 2: Counting Methods and Probability
- Objective 1: Identify events as not mutually exclusive and calculate probabilities involving events that are not mutually exclusive.
- Objective 2: Use the formulas to calculate probabilities of dependent events.
- Objective 3: Find the probability of a variety of events, from a mix of mutually exclusive and not-mutually exclusive, Or, And, and Not, and conditional events.
- Objective 4: Describe and interpret a binomial probability distribution and calculate binomial probabilities.
- Objective 5: Describe and interpret a geometric probability distribution and calculate geometric probabilities.
- Objective 6: Simulate data collection.
- Objective 7: Calculate theoretical and experimental expected value and use expected value to make real-world decisions.
- Objective 8: Develop a probability distribution for a random variable defined for a sample space in which the probabilities are calculated from empirical data.
- Objective 9: Use probability trees as an alternate method of calculating the probability of independent and dependent events.
- Objective 10: Collect data to calculate and interpret expected value and determine the mean of the associated probability distribution.
Unit 3: Counting Methods and Probability
- Objective 1: Apply the Fundamental Counting Principle and use advanced counting techniques to determine the number of permutations and combinations.
- Objective 2: Calculate the probability of an event using the Fundamental Counting Principle, permutations, and combinations.
- Objective 3: Use a normal curve to find probability of a score being less (or greater) than the score at the position of 1, 2, and 3 standard deviations from the mean.
- Objective 4: Use properties of normally distributed data to determine percentiles and number of data bounded by standard deviations.
- Objective 5: Use permutations and combinations to compute probabilities in real-world situations.
Unit 4: Forming and Testing Hypotheses
- Objective 1: Understand and apply the requirements and assumptions of associated with hypothesis testing such as null and alternative hypotheses, statistical significance, and the significance level.
- Objective 2: Use a z-test for population means and proportions.
- Objective 3: Use a t-test for population means and proportions.
- Objective 4: Identify and explain Type 1 and Type 2 errors.
- Objective 5: Understand and explain how sample size affects the confidence levels in a confidence interval.
- Objective 6: Use a chi-square test to evaluate a hypothesis.
- Objective 7: Use a paired-t test to compare means of two samples.
- Objective 8: Understand criticisms of statistical hypothesis testing.
- Objective 9: Use the chi-square goodness of fit test for real-world data to determine if the difference between expected and observed data is statistically significant.
Unit 5: Applications of Probability and Hypothesis Testing
- Objective 1: Identify when a statistical result or graph can be misleading.
- Objective 2: Apply statistical techniques for small sample sizes.
- Objective 3: Identify and give examples of ethical issues involved in selecting reporting.
- Objective 4: Examine and critique health science, government research, sports strategies, and market research studies involving statistical analysis.
- Objective 5: Identify possible issues that could lead to inconclusive results and where sample results did not reliably predict population results.
- Objective 6: Compare data from short time intervals to longitudinal data.
- Objective 7: Simulate a drug study and use statistical tests to determine if differences between parameters are significant.
Additional Resources
In addition to the default course content, some projects may require paper and pencil or drawing supplies to complete the assignment. Writing assignments may require a graphic organizer to be printed out and used in the writing process. An alternative to printing the organizer is to download the document, enter your information, save, and upload the completed organizer.
The following lessons require specific materials that are not included in this course and must be acquired separately:
Unit | Assignment | Resource |
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All | General Requirement |
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1 | Project |
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3 | Project |
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