Question

According to a recent​ survey, the population distribution of number of years of education for​ self-employed individuals in a certain region has a mean of 13.6 and a standard deviation of 5.0.

a. Identify the random variable X whose distribution is described here.

b. Find the mean and the standard deviation of the sampling distribution of x overbarx for a random sample of size 100. Interpret them.

c. Repeat​ (b) for n = 400. Describe the effect of increasing n.

Answer 1

Answer:

Given,

Mean = 13.6

Standard deviation = 5

a)

Here X is a random variable i.e., a no. of years of education for​ self-employed individuals in a certain region.

b)

sample n = 100

Mean ux = u = 13.6

Standard deviation x = /sqrt(n) = 5/sqrt(100) = 5/10 = 0.5

c)

sample n = 400

Mean ux = u = 13.6

Standard deviation x = /sqrt(n) = 5/sqrt(400) = 5/20 = 0.25

Here when sample increases then there is decrease in sampling standard deviation.