# Section 7: Hypothesis Testing

In the previous section, we developed statistical methods, primarily in the form of confidence intervals, for answering the question "what is the value of the parameter *θ*?" In this section, we'll learn how to answer a slightly different question, namely "is the value of the parameter *θ *such and such?" For example, rather than attempting to estimate *μ*, the mean body temperature of adults, we might be interested in testing whether *μ*, the mean body temperature of adults, is really 37 degrees Celsius. We'll attempt to answer such questions using a statistical method known as **hypothesis testing**.

We'll derive good **hypothesis tests** for the usual population parameters, including:

- a population mean
*μ* - the difference in two population means,
*μ*_{1}*−**μ*_{2}, say - a population variance
*σ*^{2} - the ratio of two population variances, \[\sigma^2_1/\sigma^2_2\], say
- a population proportion
*p* - the difference in two population proportions,
*p*_{1}*−**p*_{2}, say - three (or more!) means,
*μ*_{1}*,**μ*_{2}, and*μ*say_{3},

We'll also work on deriving good hypothesis tests for the slope parameter *β* of a least squares regression line through a set of (*x*,*y*) data points, as well as the corresponding population correlation coefficient \(\rho\).