4. The university is interested in determining if the proportionof graduates obtaining a first-class degree has changed from 2016to 2017. Out of 2800 graduates in 2016, 560 obtained a first classdegree. In 2017, 805 graduates out of 3500 obtained a first classdegree.
(a) Write down the method of moments estimates for theproportion of first-class degrees
in 2016 and 2017, pˆ2016 and pˆ2017.
(b) Write down appropriate null and alternative hypotheses forthis test.
(c) What assumptions are required to conduct your hypothesistest from (b), does this data satisfy them?
(d) Calculate a 90% confidence interval for the difference inthe proportion of first-class degrees awarded.
(e) Using your answer to part (d), or otherwise, test yourhypothesis from (b) at the 10% level. You should clearly state theconclusion of your test.
