Question

Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions for two groups or comparing two proportions from the same group. State whether the methods of this section apply to the difference in proportions. (a) In a taste test, compare the proportion of tasters who prefer one brand of cola to the proportion who prefer the other brand. (b) Compare the proportion of males who voted in the last election to the proportion of females who voted in the last election. (c) Compare the graduation rate (proportion to graduate) of students on an athletic scholarship to the graduation rate of students who are not on an athletic scholarship. (d) Compare the proportion of voters who vote in favor of a school budget to the proportion who vote against the budget.

Short answer

All situations require comparisons of proportions. (a) compares two different groups, as does (b) and (c). (d) compares two proportions from the same group. The methods of this section apply for all as they involve differences in proportions.

Step-by-step solution

Identify and Compare Proportions for (a)

This comparison is between two groups: one group of tasters who prefer brand A of cola and another group who prefer brand B. This is a comparison of proportions for two different groups. The methods of the section apply to the difference in proportions here.

Identify and Compare Proportions for (b)

In this case, the proportions being compared are those of males who voted in the last election and females who did. Again, these are proportions from two different groups. The methods of this section can be applied to the difference in proportions in this case as well.

Identify and Compare Proportions for (c)

Here, the proportions are of students on an athletic scholarship who graduated versus those who are not on an athletic scholarship. These are proportions from two different groups, so again, the methods outlined in the section can apply.

Identify and Compare Proportions for (d)

This situation compares proportions from the same group – voters. One proportion is of those who voted in favor of the school budget, and the second, those who voted against it. Here also, the methods of this section apply to the difference in proportions.