In the past, 60% of all undergraduate students enrolled at State University earned their degrees within 4 years of matriculation. A random sample of 36 students from the class that matriculated in the fall of 1994 was recently selected to test whether there has been a change in the proportion of students who graduate within 4 years. Administrators found that 15 of these 36 students graduated in the spring of 1998 (i.e., 4 academic years after matriculation).

a. Given the sample outcome, construct a 95% confidence interval for the relevant population proportion. Does this interval estimate suggest that there has been in a change in the proportion of students who graduate within 4 years’? Why or why not?

b. Given the sample outcome, construct a 99% confidence interval for the relevant population proportion. Does this interval estimate suggest that there has been in a change in the proportion of students who graduate within 4 years? Why or why not?