Math Problem Statement

A magazine provided results from a poll of

500500

adults who were asked to identify their favorite pie. Among the

500500

​respondents,

1212​%

chose chocolate​ pie, and the margin of error was given as

plus or minus±55

percentage points. Describe what is meant by the statement that​ "the margin of error was given as

plus or minus±55

percentage​ points."

Question content area bottom

Part 1

Choose the correct answer below.

A.

The statement indicates that the study is

​100%minus−55​%equals=9595​%

confident that the true population percentage of people that prefer chocolate pie is

1212​%.

B.

The statement indicates that the interval

12​%plus or minus±5​%

is likely to contain the true population percentage of people that prefer chocolate pie.

C.

The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval

12​%plus or minus±5%.

D.

The statement indicates that the study is only

5​%

confident that the true population percentage of people that prefer chocolate pie is exactly

12​%.

Solution

The correct answer is:

B. The statement indicates that the interval 12% ± 5% is likely to contain the true population percentage of people that prefer chocolate pie.

Explanation:

The margin of error in a poll refers to the range within which the true population value (in this case, the percentage of people who prefer chocolate pie) is likely to fall. When it is given as "±5 percentage points," it means that the true percentage of people who prefer chocolate pie could be as low as 12% − 5% = 7%, or as high as 12% + 5% = 17%. Therefore, the interval 7% to 17% is the likely range for the true population percentage of people who prefer chocolate pie.

Why the other options are incorrect:

  • A: This statement is confusing because the confidence level is not stated as 95%. The margin of error does not directly correlate with a "100% - 55% = 95%" confidence.

  • C: While it might seem like this could be correct, the statement implies that the margin of error is 5%, not 55%. The question says the margin of error is ±5 percentage points, so the true population percentage could be in the 7% to 17% range.

  • D: This is incorrect because the margin of error does not imply only 5% confidence. The margin of error refers to the range of values the true population percentage is likely to fall within, not the level of confidence.

Would you like more details on margin of error or sampling techniques?

Here are some follow-up questions to explore further:

  1. What is the meaning of a confidence interval in polling data?
  2. How does sample size affect the margin of error in a poll?
  3. What does a 95% confidence level mean in statistics?
  4. How would you calculate the margin of error if the sample size were smaller?
  5. What is the relationship between sample proportion and margin of error in surveys?

Tip: Always pay attention to the margin of error when interpreting poll results. It gives you a range where the true value is likely to fall, rather than a precise number.

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Math Problem Analysis

Mathematical Concepts

Polls
Margin of Error
Confidence Interval

Formulas

Margin of Error = Z * (Standard Deviation / √n)
Confidence Interval = Sample Proportion ± Margin of Error

Theorems

Central Limit Theorem
Confidence Interval for Proportions

Suitable Grade Level

Grades 9-12