If we knew the population mean and variance, we would expect
A) the sample mean would closely approximate the population mean.
B) the sample mean would differ from the population mean by no less than 1.96 standard deviations only 5% of the time.
C) the sample mean would differ from the population mean by no more than 1.64 standard deviations only 5% of the time.
D) the sample mean would differ from the population mean by more than 1.96 standard errors only 5% of the time.

Question

Quizplus · Accepted Answer

The sample mean would differ from the population mean by more than 1.96 standard errors only 5% of the time due to the properties of the normal distribution and the concept of confidence intervals.

If We Knew the Population Mean and Variance, We Would