The probability distribution of all possible values of the sample mean is
A) the probability density function of .
B) the sampling distribution of .
C) the grand mean, since it considers all possible values of the sample mean.
D) one, since it considers all possible values of the sample mean.

Question

The probability distribution of all possible values of the sample mean  is
A) the probability density function of . 
B) the sampling distribution of . 
C) the grand mean, since it considers all possible values of the sample mean. 
D) one, since it considers all possible values of the sample mean.

Quizplus · Accepted Answer

The probability distribution of all possible values of the sample mean is the sampling distribution of the sample mean, which is the distribution of all possible sample means that could be obtained from a population. Therefore, choice B is correct. Choice A is incorrect because the probability density function is a function that describes the likelihood of obtaining a specific value in a continuous distribution, while the sample mean is a discrete random variable. Choice C is incorrect because the grand mean is a constant value that represents the average of all measurements in a population, while the sample mean is a random variable that depends on the specific sample selected. Choice D is incorrect because the probability distribution of a random variable always sums up to one, but it doesn't imply that all possible values are equally likely to occur.

The Probability Distribution of All Possible Values of the Sample