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Which of the following estimates at a 95% confidence level most likely comes from a small sample?

A. 60% (±18%)

B. 62% (±6%)

C. 65% (±2%)

D. 71% (±4%)

User Chenyang
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1 Answer

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Final answer:

Option A, '60% (±18%)', is most likely derived from a small sample as wider confidence intervals typically indicate a larger margin of error which is associated with smaller samples.

Step-by-step explanation:

The question pertains to the width of confidence intervals and what they may imply about the size of the sample used to estimate a population parameter. Confidence intervals are ranges derived from sample data that are believed to contain the true population parameter (like the mean or proportion) with a certain level of confidence. At a 95% confidence level, a wider interval suggests more uncertainty and typically indicates that a smaller sample was used. Hence, the interval '60% (±18%)' is most likely from a small sample.

According to the properties of confidence intervals, as the confidence level increases or the sample size decreases, the margin of error (or the width of the confidence interval) generally increases. In contrast, larger samples and lower confidence levels typically result in narrower intervals. Based on this, Option A with a 36% total interval width (18% in both directions from the point estimate) most likely comes from a small sample, since its margin of error is the largest among the options given.

User Seek
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