SOLUTION: 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 of p(proportion) using an

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Question 1166449: 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 of p(proportion) using an absolute value inequality using the
Answer by CPhill(2138) About Me  (Show Source):
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The conclusion of the poll regarding the proportion ($p$) of people who prefer dark chocolate over milk chocolate can be described by the following absolute value inequality:
$$|p - 0.43| \leq 0.019$$
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## Explanation
This inequality expresses that the true proportion ($p$) is estimated to be $0.43$, with a maximum possible difference (or error) of $0.019$ in either direction.
1. **Point Estimate:** The sample proportion is $43\%$, or **$0.43$**. This is the center of the confidence interval.
2. **Margin of Error ($E$):** The error is $1.9\%$, or **$0.019$**.
3. **Absolute Value Inequality:** The standard form for a confidence interval's conclusion is:
$$|\text{True Proportion} - \text{Sample Proportion}| \leq \text{Margin of Error}$$
### Confidence Interval (Expanded Form)
The inequality can be rewritten as a compound inequality:
$$-0.019 \leq p - 0.43 \leq 0.019$$
Adding $0.43$ to all parts gives the confidence interval:
$$0.43 - 0.019 \leq p \leq 0.43 + 0.019$$
$$0.411 \leq p \leq 0.449$$
The poll concludes that the true proportion of people who prefer dark chocolate is between **$41.1\%$ and $44.9\%$**.