In the 1 Proportion test example, we have 92 students and 28 smokers in the group. The sample shows 30.4 percent of the group as smokers. The results from a 1 Proportion test will indicate that we cannot reject the null hypothesis.

For this recipe, we want to know how many students we need to sample in order to be able to observe a difference of 2.5 percent or 5 percent between the hypothesized and actual proportions that have a power of 80 percent. We will use a hypothesized proportion of 25 percent and differences of 2.5 and 5 percent.