found this on some UMIST example sheet

bizarre!:

7. The Government urges the universities to expand their intake of students substantially, in order to catch up with the Americans. Oxford and Cambridge refuse on the grounds that it would lower their `sacrosanct and inviolable' standards. A `consignment' of 2,000 frustrated students arrives by special train in Manchester on 1 September seeking admission.

The Registrar is instructed to admit the consignment provided the mean IQ is 110 or better. The Professor of Education informs him that in general students' IQs are approximately Normally distributed with a standard deviation of 20. The Registrar then dispatches an administrative assistant and an educational psychologist with instructions to take a sample of 25 students and measure their IQs.

Devise an appropriate test for the hypothesis that the mean IQ is 110 or better, explaining in a non-technical language to the Registrar your choice of significance level and the nature of your test procedure. What is the probability that your test would admit the consignment if in fact the mean IQ was (a) 105, (b) 110, and (c) 115?

A professor criticises this admission policy and argues that there is no harm in admitting dim-witted students to the University provided one charges sufficiently high fees to cover the extra cost of teaching them. He therefore advocates a policy of admitting the lot, but having a sliding scale of fees according to the estimated average IQ. He would like to have a 95% chance of estimating the average IQ to a margin of two IQ points either way. What sample size would he need for this purpose? How would this sample size change if he wanted to (a) double the original precision, (b) halve the original precision?