As the sample size increases, the confidence interval ___________ .

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BlackTom AI · Accepted Answer

The question asks how the confidence interval behaves as the sample size grows. In general, when you increase n, the standard error decreases because SE is proportional to 1 over the square root of n.

This reduction in standard error makes the margin of error smaller, which in turn makes the confidence interval narrower, assuming the confidence level and the underlying variability stay the same.

Other factors that could influence the interval width include the chosen confidence level: a higher confidence level (e.g., 99% vs 95%) widens the interval, while a lower level narrows it. Similarly, more variability in the population (higher standard deviation) tends to widen the interval for a given n.

Since the prompt provides only the stem and indicates that the answer is related to how the interval changes with sample size, the key takeaway is that, all else equal, increasing the sample size leads to a narrower confidence interval because the estimate becomes more precise.

Note: If there were multiple choices, typical correct options would express the idea that the interval becomes narrower or the margin of error decreases as n increases, while incorrect options might suggest the interval remains the same, widens, or depends on something other than sample size.

STAT 1450.02 SP2025 (28132) Checkpoint 16.3

As the sample size increases, the confidence interval ___________ .

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