Question

According to data from the United States Elections Project, only 36 percent of eligible voters voted in the 2014 elections. For random samples of size 40, which of the following best describes the sampling distribution of the (p-hat), the sample proportion of people who voted in the 2014 elections?

Answer 1

Using the Central Limit Theorem, it is found that the sample proportion of people who voted in the 2014 elections is approximately normal, with mean of 0.36 and standard error of 0.0759.

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 $s = \frac{\sigma}{\sqrt{n}}$.  

• 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 $s = \sqrt{\frac{p(1-p)}{n}}$

In this problem:

• 36% of eligible voters voted, hence $p = 0.36$.

• Samples of size 40, hence $n = 40$.

Then:

$\mu = p = 0.36$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.36(0.64)}{40}} = 0.0759$

Hence, the distribution is approximately normal, with mean of 0.36 and standard error of 0.0759.

To learn more about the Central Limit Theorem, you can take a look at brainly.com/question/16695444