### Understanding Margin of Error in Statistical PollingIn fields such as politics and marketing, estimates of a percentage or proportion \( p \) are often crucial. A key calculation in statistical polling is the margin of error, which represents the largest reasonable error that the poll could have. For example, a poll result of 72% with a margin of error of 4% suggests that \( p \) is most likely to be between 68% and 76% (calculated as 72% minus 4% to 72% plus 4%).### Example Poll AnalysisConsider a hypothetical poll where the proportion of people who prefer dark chocolate over milk chocolate is reported as 25% with a margin of error of 1.3%. To understand the conclusion about \( p \) using an absolute value inequality, we need to express this margin of error appropriately.### Using the Mobius Symbolic Entry OptionThe answer field below employs the symbolic entry option in Mobius, allowing you to type in a vertical bar \( | \) to denote absolute values. Additionally:- When you type the symbols \( < \) and then \( = \), the symbolic entry option will automatically convert this to \( \leq \).- Similarly, when you type \( > \) and then \( = \), it converts to \( \geq \).### Decimal Number UsageMake sure to use decimal numbers in your responses, such as representing 40% as 0.40.**Note:** This text helps in handling margin of error and absolute value equations, often needed in interpreting poll results and their likely ranges.

From the given data we can conclude that, Proportion = 25% Margin of error = 1.3%

Answered: In politics, marketing, etc. we often…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 6%? A previous study indicates that the proportion of households with two computers is 23%. Group of answer choices
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 44% with a margin of error of 2.2%. 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 to >.
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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 or 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 44% with a margin of error of 1.3%. Describe the conclusion about p using an absolute value inequality.
n 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 1.3%. Describe the conclusion about p using an absolute value inequality.
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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 39% with a margin of error of 1.3%. 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 to ≤ . 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%).
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