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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 34% with a margin of error of 1.6% . Describe the conclusion about p using an absolute value inequality.this is copy and pasted from my assignment



Answer :

Given: The below

[tex]\begin{gathered} ME(Margin-of-error)=1.6\% \\ proportion(p)=34\% \end{gathered}[/tex]

To Determine: The conclusion about p using an absolute value inequality

Solution

Using the absolute inequality about p using an absolute value inequality below

[tex]|p-\hat{p}|\leq ME[/tex]

Substituting the given

[tex]\begin{gathered} p-E\leq p\leq p+E \\ 34\%-1.6\%\leq p\leq34\%+1.6\% \\ 32.4\%\leq p\leq35.6\% \end{gathered}[/tex]

Hence, p is most likely going to be between 32.4% and 35.6%

(32.4% ≤ p ≤ 35.6%)

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