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 13.5 and a standard deviation of 2.8. 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 overbar for a random sample of size 49. Interpret them. c. Repeat (b) for nequals196. Describe the effect of increasing n.

a) X: number of years of education

b) Sample mean = 13.5, Sample standard deviation = 0.4

c) Sample mean = 13.5, Sample standard deviation = 0.2

d) Decrease the sample standard deviation

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 13.5 years

Standard deviation,σ = 2.8 years

a) random variable X

X: number of years of education

Central limit theorem:

If large random samples are drawn from population with mean and standard deviation , then the distribution of sample mean will be normally distributed with mean and standard deviation

b) mean and the standard for a random sample of size 49

c) mean and the standard for a random sample of size 196

d) Effect of increasing n

As the sample size increases, the standard error that is the sample standard deviation decreases. Thus, quadrupling sample size will half the standard deviation.

b

step-by-step explanation: