Question

a magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. among the 2000 respondents, 14% 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 100% - 4% = 96% confident that the true population percentage of people that prefer chocolate pie is 14%.

○ b. the statement indicates that the study is only 4% confident that the true population percentage of people that prefer chocolate pie is exactly 14%.

○ c. the statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 14% ±4%.

○ d. the statement indicates that the interval 14% ±4% is likely to contain the true population percentage of people that prefer chocolate pie.

Explanation:

• Option A: Margin of error is not directly related to confidence level in this way. Confidence level is a separate concept in statistics.
• Option B: Margin of error does not represent the confidence level of the estimate being exactly the sample proportion.
• Option C: While the interval \(14\%\pm4\%\) is part of the interpretation, it lacks the key idea of likelihood.
• Option D: The margin of error \(\pm4\) percentage points means that the interval \(14\%\pm4\%\) (i.e., \(10\%\) to \(18\%\)) is likely (based on the confidence level associated with the margin - of - error calculation) to contain the true population percentage of people who prefer chocolate pie.

Answer:

D. The statement indicates that the interval \(14\%\pm4\%\) is likely to contain the true population percentage of people that prefer chocolate pie.