Answer:
Whenever n increases we get std deviation of sample mean decreases.
Step-by-step explanation:
Given that ducation of the self-employed: according to a recent current population reports, the population distribution of number of years of education for self-employed individuals in the united states has a mean of 13.6 and a standard deviation of 3.0.
The central limit theorem says sample mean follows normal for randomly drawn samples of large sizes.
a) Hence X bar follows a normal with mean = 13.6
and std dev = std dev of sample/square root of sample size.
Hence std dev of x bar = 3/sqrt 100 = 0.3
b) when n =400 square root of n becomes double making the std dev of sample mean exactly 1/2
Hence new std dev = 3/sqrt 400 = 0.15
Whenever n increases we get std deviation of sample mean decreases.
