Question

Simple Random Sample of Size 25:

Answer 1

Answer:

By the Central Limit Theorem, it is approximately normal with mean 0.29 and standard deviation 0.0596

Step-by-step explanation:

Central Limit Theorem

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 $s = \frac{\sigma}{\sqrt{n}}$.

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 $s = \sqrt{\frac{p(1-p)}{n}}$

According to the U.S. Census Bureau, 29% of Americans age 25 years or older have already earned a bachelor's or more advanced degree.

This means that $p = 0.29$

You decide to randomly select 58 adults over the age of 25 to ask if they have earned at least a bachelor's degree.

This means that $n = 58$

Describe the sampling distribution of the proportion of respondents who have earned at least a bachelor's degree.

By the Central Limit Theorem, it is approximately normal with mean $\mu = p = 0.29$ and the standard deviation is $s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.29*0.71}{58}} = 0.0596$