Topics and goals: This course aims to provide an understanding of the nature of statistical reasoning, to formulate the presuppositions needed to make such reasoning valid, and to acquire discernment concerning the validity of statistical deductions.

Topics include:
(1) Development of the theory of specific probability distributions-normal, binomial, Poisson, hypergeometric, gamma, Chi-square, and their use in sampling theory. Starting with a random sample, deciding on appropriate objectives and techniques for obtaining a point estimate of a parameter.
(2) The study of accuracy expected from a point estimate; confidence intervals and their meaning. Comparing two populations with a similar distribution but possibly distinct parameters. How large a sample is needed? Efficiency of estimators.
(3) Hypothesis testing-two types of error to be avoided. Choice of critical region for a hypothesis test: use of Neyman-Pearson likelihood ratio criteria.
(4) Introduction to linear models and the use of ANOVA methods for testing hypotheses. Simple regression problems. First introduction to the problem of correlation.

Students in this course are expected to learn which standard method is appropriate for the particular statistical analysis problem being considered-and to be able to formulate the appropriate model for quantitative discussion of the problems. Weekly homework assignments and projects are an essential part of the course.

Relation to other courses: This is the entry-level preparatory course required before pursuing further courses in statistics such as STAT 313 (Sample Surveys); STAT 512 (Applied Linear Models); STAT 513 (Applied Multivariate Statistics); STAT 515 (Actuarial Statistics).