Define the term sampling distribution of the mean and descri

Define the term “sampling distribution” of the mean, and describe how the shape, center, and spread of the sampling distribution of the mean change as sample size increases.

Solution

The given question deals with the study of the sampling distribution, its definition, and the change in shape,center and spread with change in sample size.

The sampling distribution may be considered as the distribution of the statistic for all possible samples from the same population of a given size.The probability distribution for the statistic under study for any hypothesis test, is termed as sampling distribution.

Now the parameters of the distribution with chang in sample size is given below,

the shape of the sampling distribution will tend to be inverted V shaped as sample size increases,the spread will tend to be lower with increase in sample size, and finaly the centre will tend to coincide with the true mean of the population, as the sample size increases.