Question 1074740: A random sample will be selected from a population of rabbits. The weights of the rabbits in the sample will be measured, and the sample mean weight will be calculated. Assuming that the sample size is greater than 1, the standard deviation of the sampling distribution of the sample mean is
A. less than the population standard deviation, because the weight of any rabbit in the sample is likely to be closer to the population mean than the weight of a rabbit chosen at random from the population.
B. less than the population standard deviation, because, when calculating the sample mean, weights in the sample far from the population mean are averaged out with the other weights in the sample.
C. equal to the population standard deviation.
D. more than the population standard deviation, because there is a greater possibility of getting a weight that is far from the population mean in the sample than when picking one rabbit at random.
E. more than the population standard deviation, because using a large sample introduces a greater possibility of the sample mean being far from the population mean.
I understand that the standard deviation of the sampling distribution of the sample mean will equal the standard deviation of the population divided by root n. So does that mean the answer is either d or e?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The standard deviation is LESS than that of the population for the reason stated in B. Weights in the sample far from the mean are averaged out. While it might be possible to get something 2 sd from the mean, to get a whole sample of those 2 sd from the mean would be very unlikely.
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