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Chapter 6: Problem 160

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

Expert verified
In all four situations, a comparison of proportions is being made. Situations (a), (b), and (c) involve comparisons between two separate groups, while situation (d) involves comparison within the same group. The methods discussed apply to all four situations.

Step by step solution

01

Situation (a) Analysis

In this case, the comparison is being made between the proportion of tasters who prefer one brand of cola to the proportion who prefer the other brand. This case involves comparing proportions for two separate groups - those who prefer one brand and those who prefer the other brand. Therefore, the methods of this section apply to the difference in proportions.
02

Situation (b) Analysis

Here, the proportion of males who voted in the last election is being compared to the proportion of females who voted in the last election. This is also a comparison between two separate groups - males and females. So, the methods of this section apply to the difference in proportions.
03

Situation (c) Analysis

In this situation, the graduation rate of students on an athletic scholarship is compared to the graduation rate of students who are not on an athletic scholarship. That is, it is a comparison between two separate groups - students on athletic scholarships and those not on athletic scholarships. Hence, the methods of this section apply to the difference in proportions.
04

Situation (d) Analysis

This involves comparing the proportion of voters who vote in favor of a school budget to the proportion who vote against the budget. Here, the comparison is being made within the same group (voters). It is still acceptable to apply the methods of this section to find the difference in proportions.

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