位置5的问题 As the sample size increases, the margin of error decreases.TrueFalseSingle choice
A
True
B
False

Question

位置5的问题 As the sample size increases, the margin of error decreases.TrueFalse

BlackTom AI · Accepted Answer

In this question, we are evaluating the statement about how margin of error behaves as sample size grows.
Option 1: True. The margin of error (MOE) is typically proportional to the standard error of the estimate. For many common cases, SE = sigma / sqrt(n) (or an estimate of sigma / sqrt(n) when sigma is unknown). As n increases, sqrt(n) increases, causing SE to shrink, and since MOE = z*SE (or t*SE for some contexts), the MOE also decreases. This reflects the general principle that larger samples yield more precise estimates.
Option 2: False. Saying that the MOE does not decrease with larger samples contradicts the fundamental relationship between sample size and precision. If MOE stayed the same or increased, that would imply the estimate became less precise with more data, which is illogical in standard sampling theory. Moreover, even when using t-distributions with smaller degrees of freedom, the MOE generally declines as n grows, approaching the z-quantile scenario for large samples.
In summary, the statement that the margin of error decreases as the sample size increases aligns with the mathematical form of MOE = critical_value * (standard deviation / sqrt(n)) and is inconsistent with any scenario where MOE would not decrease with larger n.

位置5的问题 As the sample size increases, the margin of error decreases.TrueFalseSingle choice

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