Proportion of Successes and Failures

In research, when using proportions, we can never have a result higher than [latex]\hat{p} = 1[/latex].

Consider our dairy farm example. If 100 people are surveyed, there is no way we can get more than 100 “yes” answers.

This allows us to determine the proportion of failures for any given value of [latex]\hat{p}[/latex] (the proportion of successes in the sample) using the formula [latex]1 - \hat{p}[/latex].

It is also important to understand how changing the numerator or denominator of a fraction or proportion changes the overall value.