Question

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 2014 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 2018 (i.e., four academic years after matriculation).

1. Given the sample outcome, calculate 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?
2. 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.

a) What is the upper limit of a 95% confidence interval on the proportion of students who graduate in four years (three decimal place)?

b) What is the value of the z-statistic for this test (three decimal places)?

c) What is the p-value for this test (four decimal places)?

d) What statistical conclusion can administrators each regarding the proportion of students graduating in four years falling below 60% at a 5% significance level?

Answer 1