Question 1194048: A population has a mean of µ = 100 and ơ = 15. Find the mean and standard deviation of the sampling distribution of samples means with sample size n.
n = 15
n= 250
Answer by math_tutor2020(3817)   (Show Source):
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Regardless of the value of n, the mean of the sampling distribution is always gong to be mu = 100 in this case.
If n = 15, then we have this standard deviation for the sampling distribution
sigma/sqrt(n)
15/sqrt(15)
3.87298
which is approximate.
If n = 250, then,
sigma/sqrt(n)
15/sqrt(250)
0.94868
is the approximate standard deviation for the sampling distribution
As n increases, the standard deviation for the sampling distribution decreases.
Intuitively it means that as the sample gets larger, we are narrowing in on the population parameter (there's less spread as the data is getting more consistent)
Summary:
mean = 100 for each case
standard deviation = 3.87298 approximately when n = 15
standard deviation = 0.94868 approximately when n = 250
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