Subsection 3.1 Section 2: Normal Approximations for Sample Proportions
So far, all the studies you have examined have involved one categorical binary variable and the relevant statistic has been the number of successes, or equivalently the proportion of successes, where "success" is defined as the outcome you count (e.g., number of heart transplantation deaths, number of helper toys, number of correct choices) in a particular sample. You have used simulation from a coin-tossing type process to approximate probabilities (p-value, error probabilities) and you calculated exact probabilities using the binomial distribution.
Historically, when computers were less prevalent, these empirical and binomial probabilities were often cumbersome to determine and statisticians instead applied a far more convenient approximation method to estimate the probabilities of interest. In this section, you will see how the normal probability model can be used as a third method to approximate the p-values, confidence intervals, and error probabilities from the previous section. See the Probability Detour 3.3 for more information about the normal distribution.
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