SOLUTION: The Z score of the sample mean on the distribution of means is: A) different from a normal Z score because an estimated population standard deviation is used B) smaller than no

Algebra ->  Probability-and-statistics -> SOLUTION: The Z score of the sample mean on the distribution of means is: A) different from a normal Z score because an estimated population standard deviation is used B) smaller than no      Log On


   

Question 1193047: The Z score of the sample mean on the distribution of means is:
A) different from a normal Z score because an estimated population standard deviation is used
B) smaller than normal due to the reduced variance in the distribution of means
C) conceptually similar to creating a Z score from a raw score
D) equivalent to the sample mean divided by the population variance
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i would say B.
the formula for a z-score of an individual element is z = (x - m) / sd
the formula for a z-score of the mean of a sample of n elements is z = (x - m) / (sd / sqrt(n)).
z is the z-score
x is the raw score
m is the mean
sd is the standard deviation of an individual element in the distribution of elements.
(sd / sqrt(n)) is the standard deviation of the sample means in a distribution of sample means.
here's a reference on the subject.
https://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html
here's another.
http://matcmath.org/textbooks/engineeringstats/distribution-of-sample-means/