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A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 14% chose chocolate pie, and the margin of error was given as plus or minus 33 percentage points. Describe what is meant by the statement that 'the margin of error was given as plus or minus 33 percentage points.' Choose the correct answer below:
A. The statement indicates that the study is only 33% confident that the true population percentage of people that prefer chocolate pie is exactly 14%.
B. The statement indicates that the study is 100% minus 33% equals 97% confident that the true population percentage of people that prefer chocolate pie is 14%.
C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 14% plus or minus 33%.
D. The statement indicates that the interval 14% plus or minus 33% is likely to contain the true population percentage of people that prefer chocolate pie.

Answer :

In this poll, 1000 adults were asked to pick their favorite pie, and 14% chose chocolate pie. A margin of error of plus or minus 33 percentage points is given. Understanding what this means is crucial when interpreting poll results.

The margin of error reflects the range within which we can expect the true population percentage to lie, with a certain level of confidence.

The correct answer for the given options is D: "The statement indicates that the interval 14% plus or minus 33% is likely to contain the true population percentage of people that prefer chocolate pie."

Let's break this down further:

  1. What is a Margin of Error?

    • A margin of error indicates the amount of uncertainty in the results. It accounts for potential variations or errors in sampling or data collection.

  2. What is the Given Scenario?

    • In this example, 14% of the 1000 adults sampled preferred chocolate pie.

  3. Understanding Plus or Minus 33%

    • The "plus or minus 33%" means that the true proportion of the whole population who prefer chocolate pie could reasonably be as low as 14% - 33% = -19% or as high as 14% + 33% = 47%.
    • However, since a negative percentage isn't possible, it highlights that data with such a large margin is not very precise.

  4. Interpretation of the Margin of Error

    • Therefore, the margin of error tells us that with a certain confidence level (though not specified here), we believe the true preference for chocolate pie is probably somewhere between 0% and 47%.

It's essential for interpreting such results to recognize that a larger margin of error indicates less certainty about the actual population preference, and smaller margins indicate greater confidence in the accuracy of the survey results.

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Rewritten by : Barada