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Expanded Course Description
The course satisfies Science Group criteria in that it introduces both the theory and the practice of mathematical statistics. It emphasizes statistical modeling and hypothesis testing. The process of hypothesis testing (generating a hypothesis, designing an experiment to test that hypothesis along with criteria to reject the hypothesis, conducting the experiment and using the pre-decided criteria to either accept or reject the original hypothesis) is at the heart of the scientific method.
Students will learn the basic definitions of probability theory, including the definitions of discrete and continuous random variables and various definitions of spread and the proof of Chebyshev's inequality. Students will also learn about the binomial, normal and Student t random variables and the statement of the central limit theorem.
Students will learn standard techniques to estimate population parameters from statistics based on samples. In particular, students will be able to apply t-tests and z-tests as appropriate (for one and two samples) to do hypothesis testing and confidence intervals. Students will also use the Chi-squared statistic to do hypothesis testing with categorical data. Students will calculate and apply correlation coefficients and regression lines, and use regression for estimation.
Emphasis will be placed on starting with data describing non-mathematical objects and situations and on explaining answers to questions in both mathematical and non-mathematical terms.