Question

5. Many samples of the same size are taken from a population with a population proportion of 0.75. Which sample

sizes, n, would be too small to use a normal curve to approximate the sampling distribution? Select all that apply.
Answer choices: 18
30
45 60

Answer 1

18.

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(n being at least 30), the sampling distribution of the sample proportion will be approximately normal with mean
`\mu = p` and standard deviation
`s = \sqrt{(p(1-p))/(n)}`

In this question:

n has to be at least 30. So the choice that answer this question, a size of n too small to use a normal curve to approximate the sampling distribution, is 18.