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A certain region of the U.S. with over 500,000 households has a mean household income of...

A certain region of the U.S. with over 500,000 households has a mean household income of $70,000 and a standard deviation of $20,000. Economists plan to take random sample of 625 households and calculate the sample mean income ?̅ for each sample.

What is the mean and standard deviation of the sampling distribution of ?̅?

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Answer #1

Given that a certain region of the U.S. with over N = 500,000 households has a mean household income of = $70,000 and a standard deviation of = $20,000.

An Economists plan to take a random sample of n = 625 households.

So, according to the central limit theorem if a large sample of size greater than 30 are taken randomly from a large population the Sample mean od the sampling distribution will be:

and the sample standard deviation will be :

thus the mean and standard deviation of the sampling distribution of ?̅ is calculated as:

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