Question

In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 35% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality.

Answer 1

The conclusion about the proportion of people who like dark chocolate more than milk chocolate, given as 35% with a margin of error of 2.5%, can be represented by the absolute value inequality |p - 0.35| <= 0.025, indicating a likely range of 32.5% to 37.5%.

Step-by-step explanation:

In the given poll, the proportion (p) of people who prefer dark chocolate over milk chocolate was found to be 35% with a margin of error of 2.5%. To describe this conclusion about p using an absolute value inequality, we can express it as |p - 0.35| ≤ 0.025. This means the true proportion of people who prefer dark chocolate is estimated to be within 2.5 percentage points of 35%, so it could likely fall between 32.5% and 37.5%.