Question

A sample is taken and a confidence interval is constructed for the mean of the distribution. At the center of the interval is always which value?

A) The sample mean (x bar).
B) The population mean µ.
C) Neither x bar nor µ since with a sample anything can happen.
D) Both x bar and µ as long as there are not too many outliers.

Answer 1

The center of the confidence interval is always the sample mean (x bar).

Step-by-step explanation:

The center of the confidence interval is always the sample mean (x bar).

A confidence interval is a range of values that estimates the unknown population parameter, such as the population mean (µ). The sample mean (x bar) is used as an estimate for the population mean (µ) and serves as the center of the confidence interval.

In other words, the confidence interval is constructed around the sample mean, and it provides a range of values within which the population mean is likely to fall.