A Gallup Poll in 2017 found that only 32% of Americans are engaged in their work environment. The poll's margin of error was \large \pm3 percentage points at the 90% confidence level. This means that:

a. The poll used a method that gets an answer within 3% of the truth about the population 90% of the time.
b. The percent of all adults who are not engaged in work is 29% and 35%.
c. if Gallup takes another poll on this issue, the results of the second poll will lie between 29% and 35%.
Selected:d. there a 90% chance that the percent of all adults who are engaged in work is between 29% and 35%.This answer is incorrect.
e. Gallup can be 90% confident that between 29% and 35% of the sample expect to be engaged at work. 

The correct interpretation of the margin of error at a 90% confidence level is closest to **answer (a)**.

### Explanation:
The margin of error means that the estimate provided by the poll could vary within a range around the reported result, and this range captures the uncertainty of the poll's estimate. The margin of error in this case is ±3 percentage points, which means that if the poll were repeated many times, 90% of the polls would result in an estimate within 3 percentage points of the true population value.

So, **answer (a)** is correct:
- **a.** "The poll used a method that gets an answer within 3% of the truth about the population 90% of the time." — This reflects the meaning of the margin of error at the given confidence level.

The other options are incorrect for the following reasons:
- **b.** The margin of error does not state that the percent of adults who are not engaged in work is exactly between 29% and 35%. It means that the true proportion of engaged adults lies within this range.
- **c.** It is not guaranteed that any single future poll will fall between these values, as the margin of error reflects the variability in the estimate, not a fixed range for the next poll.
- **d.** This statement is inaccurate because the margin of error applies to the **sample estimate**, not the entire population. A 90% confidence level means there's a 90% chance the **true** population proportion lies within this range.
- **e.** Gallup can only be 90% confident that the **true population proportion** lies between 29% and 35%, not that the sample will fall within this range.

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### Related Questions:
1. What is the difference between a sample and a population in statistics?
2. How do you calculate the margin of error for a poll?
3. What does a 90% confidence level mean in practical terms?
4. How does the margin of error change with a larger or smaller sample size?
5. How can I interpret results when the margin of error is greater than 5%?

### Tip:
Always keep in mind that a margin of error provides a range for the estimate based on the confidence level, but it doesn't guarantee that any future sample will fall within that range. It's about the reliability of the estimation process.

A Gallup Poll in 2017 found that only 32% of Americans are engaged in their work environment. The poll's margin of error was ±3 percentage points at the 90% confidence level. This means that:

a. The poll used a method that gets an answer within 3% of the truth about the population 90% of the time.
b. The percent of all adults who are not engaged in work is 29% and 35%.
c. if Gallup takes another poll on this issue, the results of the second poll will lie between 29% and 35%.
Selected:d. there a 90% chance that the percent of all adults who are engaged in work is between 29% and 35%.This answer is incorrect.
e. Gallup can be 90% confident that between 29% and 35% of the sample expect to be engaged at work.

Learn how to interpret the margin of error in a Gallup poll, with a focus on confidence levels and statistical uncertainty. This example covers a 90% confidence level and how it relates to poll estimates, including how to properly interpret the results of a margin of error in a population estimate. Suitable for high school students in Grades 10-12.

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