Which of the following increases the margin of error?

Question

BlackTom AI · Accepted Answer

The prompt asks which factor increases the margin of error. In this case, the provided correct option is 'A larger standard deviation.'
First, consider what margin of error represents: it is a range around a sample statistic (like a mean) within which the true population parameter is expected to lie a certain proportion of the time. Several components influence this width, with the standard deviation (or variability) being a key driver.
When the standard deviation increases, the spread of individual observations is wider, which makes the sample mean (and other statistics) less precise. This leads to a broader confidence interval and thus a larger margin of error.
Next, although not supplied here, it’s helpful to recall how sample size interacts: increasing the sample size tends to reduce the margin of error, since more data tends to stabilize the estimate. Conversely, decreasing n would increase the margin of error, all else equal.
Additionally, other factors like the chosen confidence level affect the margin of error: a higher confidence level (e.g., 99% vs 95%) expands the interval, increasing the margin of error as well. However, among the commonly cited drivers, larger standard deviation directly widens the MOE.
Given that the only option presented is 'A larger standard deviation,' this choice aligns with the standard statistical understanding that more variability in the data leads to less precision and a larger margin of error.

STAT 1450.02 SP2025 (28132) Checkpoint 16.4

Which of the following increases the margin of error?

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