Question

a magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. among the 1000 respondents, 12% chose chocolate pie, and the margin of error was given as ±4 percentage points. describe what is meant by the statement that \the margin of error was given as ±4 percentage points.\
choose the correct answer below.
○ a. the statement indicates that the study is only 4% confident that the true population percentage of people that prefer chocolate pie is exactly 12%.
○ b. the statement indicates that the study is 100% - 4% = 96% confident that the true population percentage of people that prefer chocolate pie is 12%.
○ c. the statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 12% ± 4%.
○ d. the statement indicates that the interval 12% ± 4% is likely to contain the true population percentage of people that prefer chocolate pie.

Explanation:

• Option A: Margin of error is not about confidence level in this way. Confidence level is a separate concept (commonly 95% etc., not related to margin of error value as \(4\%\) here in terms of confidence).
• Option B: The sample proportion is \(12\%\), but due to margin of error, the population proportion is not exactly \(12\%\).
• Option C: It doesn't state that the population proportion is in the interval. The correct interpretation is about the interval likely containing the population proportion.
• Option D: The margin of error \(\pm4\) percentage points means that the interval \(12\%\pm4\%\) (i.e., \(8\%\) to \(16\%\)) is likely (based on the confidence level associated with the margin - of - error calculation, usually \(95\%\) confidence in such polls) to contain the true population percentage of people who prefer chocolate pie.

Answer:

D. The statement indicates that the interval \(12\%\pm4\%\) is likely to contain the true population percentage of people that prefer chocolate pie.