Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?
A)A non-normal population with a large sample and an unknown population variance.
B)A normal population with a large sample and a known population variance.
C)A non-normal population with a small sample and an unknown population variance.
D)A normal population with a small sample and an unknown population variance.

Question

Quizplus · Accepted Answer

When dealing with a non-normal population and a small sample size, if the population variance is unknown, it becomes impossible to accurately construct a confidence interval for the population mean using standard methods. This is because the central limit theorem, which allows for the approximation of the sampling distribution of the sample mean to be normal for large sample sizes, does not apply, and without knowing the population variance, we cannot accurately estimate the standard error.

Under Which of the Following Circumstances Is It Impossible to Construct