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 ______.

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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 [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem, we have that:

[tex]p = 0.37, n = 35[/tex]

So

[tex]s = \sqrt{\frac{0.37*0.63}{35}} = 0.0816[/tex]

The standard deviation of this sampling distribution would equal 0.0816