Question 630178: Can someone please assit me with this? I am not getting this at all.
An April 2004 article on Hear The Issues.com stated that Americans have an average of 2.24 televisions per household (source: Nielsen Media Research). If the standard deviation for the number of televisions in a U.S. household is 1.2 and a random sample of 80 American households is selected, the mean of this sample belongs to a sampling distribution.
- What is the mean and standard deviation of this sampling distribution?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! distribution of sample means is a tough concept to grasp.
the theory is that, if you took a large number of samples of the same size and then took the mean of each of those samples, you would form a distribution of sample means.
the mean of all those sample means would be equal to the population mean.
the standard deviation of all those sample means would be equal to the population standard deviation divided by the square root of the sample size.
in your problem this comes out to be:
mean of distribution of sample means is equal to 2.24 (the population mean).
standard deviation of distribution of sample means is equal to 1.2 / sqrt(80) which is equal to .134164079
the statement "the mean of this sample belongs to a sampling distribution" alludes to the fact that this sample is one of the many samples of this same size that could be taken from the same population.
the mean of this sample might be different from 2.24, but if you took many samples of this same size and then took the mean of the mean of all of these samples, you would come up with the mean of the distribution of sample means which would be the same as the population (or very close to it - in theory it would be the same, in practice it would be very close but never right on).
if the sample size is very large, then the distribution of sample means will have a smaller standard deviation. this fact is confirmed by the equation for standard deviation of the distribution of sample means.
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