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) 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.
E) A non-normal population with a large sample and an unknown population variance and a normal population with a large sample and a known population variance.

Question

Quizplus · Accepted Answer

For a non-normal population with a small sample size and an unknown population variance, it's impossible to accurately construct a confidence interval for the population mean because the Central Limit Theorem (which allows for the approximation of the sampling distribution of the sample mean to be normal under 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