Question

Which one of the following is NOT a characteristic of the sampling distribution of a sample mean? The distribution of the values is obtained by repeated sampling. The samples are all of size n. The samples are all drawn from the same population. The mean is zero and the standard deviation is one.

Answer 1

Answer:

The mean is zero and the standard deviation is one.

Correct, since the sample mean is not always defined by a distribution with mean 0 and deviation 1. Since the normal standard distribution is not always representative of the sample mean dsitribution

Step-by-step explanation:

For this case we want to analyze the distribution of the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

Let's analyze one by one the possible options:

The distribution of the values is obtained by repeated sampling.

False, for this case we assume that the data of each observation $X_i$ , $i =1,2,...,n$ is obtained from a repated sampling method

The samples are all of size n.

False, for this case we assume that the sample mean is obtained from n data values

The samples are all drawn from the same population.

False, for this case we assume that the data comes from the same distribution

The mean is zero and the standard deviation is one.

Correct, since the sample mean is not always defined by a distribution with mean 0 and deviation 1. Since the normal standard distribution is not always representative of the sample mean dsitribution