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

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) (Show Source): You can put this solution on YOUR website!
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:
$$|p - 0.43| \leq 0.019$$
---
## 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 $44.9\%$**.
RELATED QUESTIONS
Dear Sir/Madam, I need your help. In a survey, the ratio of the number of people who (answered by Simnepi)

Define your variables, write a system of equations, use your calculator to solve the... (answered by josgarithmetic)

You get a box of assorted chocolates for Christmas. There are the following types; 8... (answered by stanbon)

You get a box of assorted chocolates for Christmas. There are the following types; 8... (answered by venugopalramana)

You get a box of assorted chocolates for Christmas. There are the following types; 8 dark (answered by Ultimatemagic)

A box of chocolates contains only milk, dark and white chocolates. The probability of... (answered by greenestamps,VFBundy)

A box contains 10 chocolates, of which 4 are dark chocolates and 6 are milk chocolates.... (answered by ikleyn)

A box of chocolates contains three milk chocolates, five dark chocolates, and three... (answered by ikleyn)

A company that supplies bulk candy to bakeries has one batch of chocolate chips that are (answered by stanbon,Finavon)