Question 1166449
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 $44.9\%$**.