Question

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) Find the mean and standard deviation of the sampling distribution of x^^\_ for a random sample of size n = 100. x^^\_ = x^^\_ = (b) Repeat (a) for n = 400. x^^\_ = x^^\_ = (c) Which of the following most closely describes the effect of increasing sample size n on the sampling distribution of sample mean? The mean of the sampling distribution stays the same, but the standard deviation decreases. The mean of the sampling distribution stays the same, but the standard deviation increases. Both the mean and the standard deviation of the sampling distribution decrease. Both the mean and the standard deviation of the sampling distribution increase.

Answer 1

a)
`\mu = 13.6, s = 0.3`

b)
`\mu = 13.6, s = 0.15`

c) Option A) The mean of the sampling distribution stays the same, but the standard deviation decreases

Explanation:

We are given the following in the question:

Population mean,
`\mu` = 13.6

Standard deviation,
`\sigma` = 3.0

a) Sample size, n = 100

The mean of the sampling distribution is best approximated by population mean.

`\bar{x} = \mu = 13.6`

`s= (\sigma)/(√(n)) = (3.0)/(√(100)) = 0.3`

b) Sample size, n = 400

The mean of the sampling distribution is best approximated by population mean.

`\bar{x} = \mu = 13.6`

`s= (\sigma)/(√(n)) = (3.0)/(√(400)) = 0.15`

c) Thus, we observed as the sample size increases the standard deviation increases.

Thus, the correct answer is:

Option A) The mean of the sampling distribution stays the same, but the standard deviation decreases