Question

4. The university is interested in determining if the proportion of graduates obtaining a first-class degree has changed from 2016 to 2017. Out of 2800 graduates in 2016, 560 obtained a first class degree. In 2017, 805 graduates out of 3500 obtained a first class degree.

1. (a) Write down the method of moments estimates for the proportion of first-class degrees
   in 2016 and 2017, pˆ2016 and pˆ2017.

2. (b) Write down appropriate null and alternative hypotheses for this test.

3. (c) What assumptions are required to conduct your hypothesis test from (b), does this data satisfy them?

4. (d) Calculate a 90% confidence interval for the difference in the proportion of first-class degrees awarded.

5. (e) Using your answer to part (d), or otherwise, test your hypothesis from (b) at the 10% level. You should clearly state the conclusion of your test.

Answer 1

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