Question

In a recent study of Vietnam veterans, researchers found that among the population of veterans, .37 have been divorced at least once. If I took all possible samples of size n= 35 from this population, calculated the sample proportion on each sample, and arranged the sample proportions into a frequency distribution, the standard deviation of this sampling distribution would equal ______.

Answer 1

The standard deviation of this sampling distribution would equal 0.0816

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the mean of the sampling proportions is p and the standard deviation is
`s = \sqrt{(p(1-p))/(n)}`

In this problem, we have that:

`p = 0.37, n = 35`

So

`s = \sqrt{(0.37*0.63)/(35)} = 0.0816`

The standard deviation of this sampling distribution would equal 0.0816