What is the difference between the Sampling Distribution of a Proportion and theSampling Distribution of a...

What is the difference between the Sampling Distribution of a Proportion and theSampling Distribution of a Mean? (3 points)

What is the mean of the sample means? (2 points)

What is the standard deviation of the sample means? (2 points)

Solutions

Expert Solution

(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 =

where is the standard deviation of population and n is the sample size.

orchestra answered 10 months ago

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