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 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.
