In Example 3.1, we see that \(27.5 \%\) of US adults are college graduates.

(a) Use StatKey or other technology to generate a sampling distribution for the sample proportion of college graduates using a sample size of \(n=50\). Generate at least 1000 sample proportions. Give the shape and center of the sampling distribution and give the standard error.

(b) Repeat part (a) using a sample size of \(n=500\).

Data From Example 3.1:

The US Census states that 27.5% of US adults who are at least 25 years old have a college bachelor’s degree or higher. Suppose that in a random sample of n = 200 US residents who are 25 or older, 58 of them have a college bachelor’s degree or higher. What is the population parameter? What is the sample statistic? Use correct notation for each answer.