Question

Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. If we repeatedly obtain random samples of 100 adults, what will be the mean of the sampling distribution of sample proportions

Answer 1

The mean of the sampling distribution of sample proportions will be 0.2

Explanation:

Central Limit Theorem for Proportions:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
`\mu = p` and standard deviation
`s = \sqrt{(p(1-p))/(n)}`

20% of American adults ages 25 and older had never been married.

This means that
`p = 0.2`

So the mean of the sampling distribution of sample proportions will be 0.2