In the past, 60% of all undergraduate students enrolled at State University earned their degrees within four years of matriculation. A random sample of 95 students from the class that matriculated in the fall of 2008 was recently selected to test whether there has been a change in the proportion of students who graduate within four years. Administrators found that 40 of these 95 students graduated in the spring of 2012 (i.e., four academic years after matriculation).
a. Given the sample outcome, find a 95% confidence interval for the relevant population proportion. Does this interval estimate suggest that there has been a change in the proportion of students who graduate within four years? Why or why not?
b. Suppose now that State University administrators want to test the claim made by faculty that the proportion of students who graduate within four years at State University has fallen below the historical value of 60% this year. Use this sample proportion to test their claim. Report a p-value and interpret it.