Question

Consider random samples of size 1200 from a population with proportion 0.65 . Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places.

Answer 1

The standard error of the distribution of sample proportions is of 0.014.

Explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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 sampling distribution of the sample proportion will be approximately normal with mean
`\mu = p` and standard deviation
`s = \sqrt{(p(1-p))/(n)}`

Consider random samples of size 1200 from a population with proportion 0.65 .

This means that
`n = 1200, p = 0.65`

Find the standard error of the distribution of sample proportions.

This is s. So

`s = \sqrt{(0.65*0.35)/(1200)} = 0.014`

The standard error of the distribution of sample proportions is of 0.014.