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

Question

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)

查看解析

登录即可查看完整答案

类似问题

If we change a 95% confidence interval estimate to a 90% confidence interval estimate, we can expect the _____.

The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____.

What value of z should you use for a 99% confidence interval for the difference of two population proportions?

A 97% confidence interval for the difference 𝜇 1 − 𝜇 2 is (4.2, 5.8). If you were to change the confidence level to 93% instead, which of the following could represent a plausible interval?

Which of the following results in a wider confidence interval? Assume the sample proportion stays the same.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单