Question

education 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.a. identify the random variable x whose population distribution is described here.b. find the mean and standard error of the sampling distribution of _x for a random sample of size 100. interpret the results.c. repeat (b) for n= 400. describe the effect of increasing n.

Answer 1

Whenever n increases we get std deviation of sample mean decreases.

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.