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 (reasonable) 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 27% with a margin of error of 1.6%. 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 too ≤ . In 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

|0.254 ≤ p ≤ 0.286|

Explanation:

Given that:

In a made up poll :

Proportion of people who like dark chocolate than milk chocolate (p) = 27%

Margin of Error = 1.6%

Hence,

p ± margin of error

27% ± 1.6%

(27 - 1.6)% ; (27 + 1.6)%

25.4% ; 28.6%

0.254 ; 0.286

Therefore ;

Lower bound = 0.254

Upper bound = 0.286

Expressing p as an absolute value Inequality ;

|0.254 ≤ p ≤ 0.286|