Question 1198132: Consider a population with a mean of 25 and a standard deviation of 4.
A sample of 100 people is taken from the above population.
What is the standard deviation of the 100-person sampling distribution
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answer: 0.40
Explanation:
n = 100 = sample size
sigma = 4 = standard deviation
SE = standard error
SE = standard deviation of the xbar distribution
SE = sigma/sqrt(n)
SE = 4/sqrt(100)
SE = 4/10
SE = 0.40
The xbar distribution refers to the distribution of sample means (xbar). In this case, we sample 100 people at random, compute the xbar of said sample, and that value is tossed into the distribution. Do this enough times and you'll get a dot plot to help form some kind of distribution curve.
As n gets larger, the xbar distribution starts to resemble the normal distribution, aka gaussian distribution. See the central limit theorem in statistics.
The standard error tells us how spread out the xbar distribution would be. The larger the SE value, the more spread out the data values are.
|
|
|
