Section 1: Estimation

In this section, we'll find good "point estimates" and "confidence intervals" for the usual population parameters, including:

  • a population mean, \(\mu\)
  • the difference in two population means, \(\mu_1-\mu_2\)
  • a population variance, \(\sigma^2\)
  • the ratio of two population variances, \(\dfrac{\sigma_1^2}{\sigma^2_2}\)
  • a population proportion, \(p\)
  • the difference in two population proportions, \(p_1-p_2\)

We will work on not only obtaining formulas for the estimates and intervals, but also on arguing that they are "good" in some way... unbiased, for example. We'll also address practical matters, such as how sample size affects the length of our derived confidence intervals. And, we'll also work on deriving good point estimates and confidence intervals for a least squares regression line through a set of \((x,y)\) data points.