In a random sample of 2872
Americans 18
and older, 27%
of participants reported they were unmarried. Use the rule of thumb to calculate the margin of error for a 95%
confidence interval. Round to the nearest hundredth, if necessary.

To calculate the margin of error (MOE) for a 95% confidence interval using the rule of thumb, you can use the formula for the margin of error for a proportion:

\[ \text{MOE} = \frac{1}{\sqrt{n}} \]

where \( n \) is the sample size. In this case, the sample size \( n \) is 2872.

1. Calculate the square root of the sample size:

\[ \sqrt{2872} \approx 53.58 \]

2. Take the reciprocal of this value:

\[ \frac{1}{\sqrt{2872}} \approx \frac{1}{53.58} \approx 0.0187 \]

3. Round to the nearest hundredth:

\[ 0.0187 \approx 0.02 \]

Thus, the margin of error for a 95% confidence interval is approximately 0.02 or 2%.

Would you like any more details or have any questions?

Here are 5 more questions you might be interested in:

1. How do you construct a 95% confidence interval for a proportion?
2. What is the interpretation of a 95% confidence interval?
3. How does the sample size affect the margin of error?
4. What are the assumptions behind the rule of thumb for margin of error?
5. Can you explain the difference between margin of error and standard error?

**Tip:** Always remember that increasing your sample size decreases your margin of error, leading to more precise estimates.

Learn how to calculate the margin of error (MOE) for a 95% confidence interval with a detailed example. Understand the formula MOE = 1 / sqrt(n) and apply it to a sample size of 2872 Americans. Get precise calculations and a rounded result. Ideal for undergraduate students and researchers.

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