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 43% with a margin of error of 1.9%. Describe the conclusion about p using an absolute value inequality.

The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in << and then, the symbolic entry option will automatically convert that to <.I the same way, if you type in> and then, the symbolic entry option will automatically convert that to >

Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).

Answer 1

The absolute value inequality is given as |(p - 0.43)I ≤ 0.019

How to describe the proportion using the absolute value inequality

The proportion p = 43% = 0.43

Margin of error = 1.9% = 0.019

The value of the proportion can then be said to lie between

(0.43 - 0.019) ≤ p ≤ (0.43 + 0.019)

In order to convert to the absolute inequality we would be having

-0.019 ≤ (p - 0.43) ≤ 0.019

I (p - 0.43)I ≤ 0.019

Read more on margin of error here

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