The U.S. Census Bureau reported that in 2015, the proportion of adult Americans age 25 and older who have a bachelor’s degree or higher is 0.325 (“Educational Attainment in the United States: 2015,” census.gov, retrieved January 22, 2017). Consider the population of all adult Americans age 25 and over in 2015 and define p̂ to the proportion of people in a random sample from this population who have a bachelor’s degree or higher.

a. Would p̂ based on a random sample of only 10 people from this population have approximately a normal distribution? Explain why or why not.

b. What are the mean value and standard deviation of p based on a random sample of size 400?

c. Suppose that the sample size is n = 200 rather than n = 400. Does the change in sample size affect the mean and standard deviation of the sampling distribution of p̂? If so, what are the new values for the mean and standard deviation? If not, explain why not.