Course title
MathPre-requisite
Algebra IICourse description
This course is designed as a 4th year math credit for students seeking a class that prepares them for college courses that involve statistical reasoning. This 21st Century skill is a reflection of the increasingly data driven world we live in. The statistical reasoning in a context that is rich with examples is likely to spark student interest. The sports-based approach is a way to add interest to the traditional statistics curriculum; extend and deepen learning; and provide real-world applications for core statistical knowledge to better engage students in their learning.
This course teaches students how to use four-steps of the statistical process in the context of sports: ask questions; collect data; analyze data; and make conclusions. Each chapter will begin with a sports-related statistical question (e.g.; Is there a home field advantage in the NFL?) and then students will learn how to collect appropriate data; how to analyze the data; and how to make reasonable conclusions. Although the context of the examples and exercises will be sports related; the primary focus of the class will be to teach students the basic principles of statistical reasoning. Major statistical topics include: analyzing distributions of univariate and bivariate data; both categorical and numerical; using graphs and summary statistics; correlation and least squares regression; using simulations to estimate probability distributions; theoretical probability distributions; including the binomial and normal distributions; rules of probability; including conditional probability and expected value; the logic of hypothesis testing; including stating hypotheses; calculating and interpreting p-values; drawing conclusions; and Type I and Type II errors; using confidence intervals to estimate parameters; and proper methods of data collection; including sampling and experimentation. Use of technology; including online applets and the graphing calculator will be prominent in the course. Throughout the course; students will complete investigations that require students to complete the four-step statistical process using athletes of their choice.
Goals To Be Addressed By This Course
Course goals and major student outcomes
* Students are able to formulate statistical questions and identify statistical claims made by others.
* Students can collect appropriate data to answer statistical questions; including designing experiments and using available data from the internet and other sources.
* Students can use a wide variety of tools to analyze and summarize distributions of data.
* Students understand the role of variability in the data collection process and incorporate this understanding when drawing conclusions about statistical questions.
* Students critically reflect on their own conclusions and conclusions made by others; including the limitations of these conclusions.
Course Objectives
Students will be able to:
* Ask statistical questions and decide which type of data collection procedure is most appropriate in a given situation
* Collect data using online databases in an efficient and effective manner
* Describe the importance of random sampling and the difference between samples and populations
* Design experiments and understand the purpose of control; randomization; replication; and blinding
* Explain how using paired data can provide better results in experiments and observational studies
* Understand when it is appropriate to conclude that changes in one variable cause changes in another variable
* Critically reflect on the limitations of their own conclusions and conclusions made by others
* Summarize distributions of data with appropriate visual displays; including pie charts; bar charts; segmented bar charts; dotplots; histograms; boxplots; and timeplots
* Calculate and interpret summary statistics for numerical data; including the mean; median; range; quartiles; interquartile range; mean absolute deviation and standard deviation.
* Identify unusual values (outliers) in a distribution and understand their effect on summary statistics
* Compare distributions of numerical data; including comparisons of shape; center and spread.
* Use standardized scores to compare athletic performances measured on different scales
* Summarize the relationship between two quantitative variables; using scatterplots; the correlation coefficient; least squares regression lines; and standard deviation of the residuals; and how these measures are affected by unusual values (outliers)
* Explain the principle of least squares
* Describe the concept of regression to the mean
* Design and conduct simulations to estimate probability distributions; by hand and with technology
* Describe the law of large numbers and its role in simulation
* Explain the concept of independence
* Use the Normal distribution and binomial distribution to estimate probabilities
* Describe the relationship between statistics and parameters in the context of sports
* Explain the concept of sampling variability in the context of sports and its role in the decision making process
* State hypotheses; including a null and alternative hypothesis; about a single proportion; the difference between two proportions; independence of athletic performances; the difference between two means or medians; the mean difference; the difference between two standard deviations; the correlation coefficient; and the slope of a least squares regression line
* Use hands-on methods and technology to simulate the distribution of a single proportion; the difference between two proportions; the longest streak; the number of streaks; the difference between two means or medians; the mean difference; the difference between two standard deviations; the correlation coefficient; and the slope of a least squares regression line
* Estimate and interpret p-values using the results of simulations
* Use p-values to make appropriate conclusions about hypotheses
* Describe a Type I and Type II error in the context of a study and how to reduce the probability that they occur
* Calculate and interpret a confidence interval for a single proportion; a single mean (or mean difference); the difference between two proportions; and the difference between two means
* Use confidence intervals to make decisions
School Country
United StatesSchool state
ArizonaSchool city
PhoenixSchool Address
N/ASchool zip code
85012Requested competency code
MathDate submitted
Approved
YesApproved competency code
- MTHA
- 4 years of Math