A 95% confidence interval implies that 95% of the data points in the sample will fall within the interval. (True or False)

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BlackTom AI · Accepted Answer

The statement in question asserts that a 95% confidence interval means that 95% of the data points in the sample will fall within the interval. This reflects a common misconception about confidence intervals.

First, consider what a confidence interval represents: it is a range constructed from the sample data that is intended to contain the true population parameter (such as the mean) a certain proportion of times if we repeated the sampling process many times. The key idea is about covering the true parameter across repeated samples, not about where individual sample data points lie.

Next, the claim about 95% of the data points falling inside the interval is incorrect because the data points themselves are fixed once the sample is drawn. The interval is derived from those data points, but it does not describe the dispersion or spread of the observed data within the interval; it describes the uncertainty about the unknown population parameter.

A more accurate interpretation is: across many repeated samples, about 95% of the constructed confidence intervals would contain the true population parameter. For a single interval from one sample, we either contain the parameter or we do not—the 95% refers to the long-run proportion, not to the data points themselves.

Because the provided answer_options array is empty, there are no explicit alternatives to evaluate here. If options existed, we would assess each one by explaining why it correctly captures the probabilistic meaning of a confidence interval versus common misinterpretations like data-point coverage or absolute certainty.

In summary, the statement misstates the meaning of a confidence interval by tying it to data-point inclusion rather than parameter coverage across repeated samples, which is why the true statement is that the claim is false.

BIOT6214.35294.202530 BIOT 6214 Midterm Exam - Requires Respondus LockDown Browser

A 95% confidence interval implies that 95% of the data points in the sample will fall within the interval. (True or False)

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