Question: A joint project of the U.S. Census Bureau and the National Science Foundation shows that people with a bachelor's degree who transferred from a community college earn less than those who start at a four-year school (USA Today, March 17, 2009). Previous studies referred to this occurrence as a "community college penalty." Lucille Barnes uses the following information to determine if a similar pattern applies to her university. She believes that the population standard deviation is $4,400 for graduates with an associate degree and $1,500 for graduates with no associate degree.
a. Set up the hypotheses to test if the report's conclusion also applies to Lucille's university.
b. Calculate the value of the test statistic and its p-value.
c. At the 5% significance level, can we conclude that there is a "community college penalty" at Lucille's university?