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University Of Central Florida (UCF) QMB3200 Quantitative Business Tools II Final Practice Exam

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What occurs to the interval estimate as the sample size increases?
Correct Answer:
The interval narrows
Explanation:
As the sample size increases, the interval estimate narrows due to the relationship between sample size and the standard error of the estimate. In statistical terms, the standard error decreases as the sample size increases, as it is calculated by dividing the standard deviation by the square root of the sample size. This reduction in standard error means that the confidence interval, which is typically constructed using the standard error, will also decrease in width. This reflects increased precision in estimating the population parameter, as a larger sample provides more reliable information about the population. Thus, a larger sample allows us to make more precise estimates, leading to a narrower interval estimate, which makes option B the correct choice.

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