In: Statistics and Probability
(a) Sampling Distribution of a Proportion is defined as follows:
If repeated random samples of a given size n are taken from a
population of values for a categorical variable,
where the proportion in the category of interest is p, then the
mean of all samples () is the
population proportion (p).
Sampling Distribution of a Mean is defined as follows:
If repeated random samples of a given size n are taken from a
population of values for a numerical variable,
where the proportion in the category of interest is , then the
mean of all samples (
) is the
population mean (
).
Thus, sampling distribution of a proportion is for categorical variable and the sampling distribution of mean is for numerical variable.
(b) Mean of sample means = Population mean =
(c) Standard deviation of sample means = /
where is the standard
deviation of population and n is the sample size.