In the past, 60% of all undergraduate students enrolled at the State University earned their degrees in four years of matriculation. A random sample of 95 students from class that matriculated in fall of 2006 was recently chosen to test whether there has been the change in the proportion of students who graduate in four years. Administrators found that 40 of these 95 students graduated in the spring of 2010 (i.e., four academic years after matriculation).
a. Given 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. Assume 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. Report a p-value and interpret it.
FYI, the four-year graduation rate for first-time, full-time freshmen entering OU in fall 2006 was 36.6% (the five-year graduation rate for fall 2005 freshmen was 62%, the largest it has been (probably) ever).