Subsection 4.1.1 Normal distribution model We will use it in data exploration and to solve important problems in statistics. The normal distribution, while never perfect, provides very close approximations for a variety of scenarios. Many variables are nearly normal, but none are exactly normal. Variables such as SAT scores and heights of US adult males closely follow the normal distribution. Indeed it is so common, that people often know it as the normal curve or normal distribution, 1 It is also introduced as the Gaussian distribution after Frederic Gauss, the first person to formalize its mathematical expression. The symmetric, unimodal, bell curve is ubiquitous throughout statistics. Inference for the slope of a regression lineĪmong all the distributions we see in practice, one is overwhelmingly the most common.Fitting a line by least squares regression.Line fitting, residuals, and correlation.Comparing many means with ANOVA (special topic).Difference of two means using the \(t\)-distribution.Inference for a single mean with the \(t\)-distribution.Homogeneity and independence in two-way tables.Testing for goodness of fit using chi-square.Sampling distribution of a sample proportion.Case study: gender discrimination (special topic).Observational studies and sampling strategies.Case study: using stents to prevent strokes.OpenIntro, online resources, and getting involved.
