To understand the relationship between sample size and margin of error, it's important to note that as the sample size increases, the margin of error decreases. The margin of error is commonly calculated using the formula:
\[ \text{Margin of Error} = z \times \sqrt{\frac{p(1-p)}{n}} \]
where:
- \( z \) is the z-score associated with the confidence level,
- \( p \) is the estimated proportion (if applicable), and
- \( n \) is the sample size.
If we don't have the specifics of the parameters (like the confidence level or estimated proportion) provided, we can only discuss the general trend. For larger sample sizes, we would expect a smaller margin of error, assuming the other parameters remain constant.
Given the options and the sample size of 480:
- 0.002
- 0.04
- 0.05
- 0.004
If we consider typical margins of error for a reasonable range of confidence intervals and sample sizes, a margin of error of either 0.04 or 0.05 would be too large for a sample size of 480, depending on the proportion being estimated. The smaller values like 0.002 and 0.004 are more reasonable.
The correct margin of error is not calculable without the proportion \( p \) and confidence level (z-score). However, if you are looking for a typical response based on common thresholds, one of the lower values (0.002 or 0.004) would be correct.
Ultimately, without additional context or parameters, the exact margin of error cannot be definitively determined. If required to choose, I would suggest going with 0.004 as a more plausible margin of error for larger sample sizes.