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A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. Among the 1500 respondents, 14% chose chocolate pie, and the margin of error was given as pm 4 percentage points. Describe what is meant by the statement that "the margin of error was given as pm 4 percentage points."

User QKWS
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Final answer:

The margin of error of ± 4 percentage points implies that the actual percentage of adults who prefer chocolate pie could be 4 percentage points higher or lower than the reported 14%. This statistical term is crucial for assessing the precision and reliability of poll results.

Step-by-step explanation:

The phrase "the margin of error was given as ± 4 percentage points" means that in the poll of 1500 adults about their favorite pie, where 14% chose chocolate pie, the true percentage of all adults preferring chocolate pie could plausibly range from 10% to 18%. This range is due to potential sampling errors which can cause the poll results to differ from the true population values.

The margin of error is a statistic expressing the amount of random sampling error in a poll's results. It represents the extent to which the poll results might deviate from the actual opinions held by the entire population, assuming a certain confidence level (often 95%). For instance, if a poll shows a candidate's support at 30% with a margin of error of ±6%, the candidate's true support could realistically fall between 24% and 36%.

The reliability of polls is greatly affected by the size of the sample and the margin of error. A smaller margin of error generally indicates a more precise poll, but other factors such as the sampling method and poll design also play significant roles in a poll's accuracy. Additionally, changes in confidence levels will affect the width of a poll's confidence intervals: increasing the confidence level results in wider intervals, while decreasing it results in narrower intervals.

User Rami Ma
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