Probability and Statistics IV: Confidence Intervals and Hypothesis Tests

This course covers two important methodologies in statistics – confidence intervals and hypothesis testing. Confidence intervals are encountered in everyday life, and allow us to make probabilistic statements such as: “Based on the sample of observations we conducted, we are 95% sure that the unknown mean lies between A and B,” and “We are 95% sure that Candidate Smith’s popularity is 52% +/- 3%.” We begin the course by discussing what a confidence interval is and how it is used. We then formulate and interpret confidence intervals for a variety of probability distributions and their parameters. Hypothesis testing allows us to pose hypotheses and test their validity in a statistically rigorous way. For instance, “Does a new drug result in a higher cure rate than the old drug” or “Is the mean tensile strength of item A greater than that of item B?” The second half the course begins by motivating hypothesis tests and how they are used. We then discuss with the types of errors that can occur with hypothesis testing, and how to design tests to mitigate those errors. Finally, we formulate and interpret hypothesis tests for a variety of probability distributions and their parameters. Hypothesis testing allows us to pose hypotheses and test their validity in a statistically rigorous way. For instance, “Does a new drug result in a higher cure rate than the old drug” or “Is the mean tensile strength of item A greater than that of item B?” The second half the course begins by motivating hypothesis tests and how they are used. We then discuss with the types of errors that can occur with hypothesis testing, and how to design tests to mitigate those errors. Finally, we formulate and interpret hypothesis tests for a variety of probability distributions and their parameters.