A survey of alumni that graduated between 2000 and 2005 from the chemical engineering department of a University in the Mid-Atlantic region of the US involved 150 randomly selected individuals: 100 BS graduates and 50 MS graduates. (The PhD graduates participated in a different survey.) The survey showed, among other things, that 9.5% of BS graduates and 4.5% of MS graduates were unemployed for at least one year during this period.

(i) If the corresponding national unemployment averages for all BS and MS degree holders in all engineering disciplines over the same period are, respectively, 15.2% and 7.5%, perform appropriate hypothesis tests to determine whether or not the chemical engineering alumni of this University fare better in general than graduates with corresponding degrees in other engineering disciplines.

(ii) Does having an advanced degree make any difference in the unemployment status of the alumni of this University? Support your answer adequately.

(iii) In connection with (ii) above, if it is desired to determine any true difference between the unemployment status of this University's alumni to within ±0.5% with 95% con?dence, how many alumni would have to be sampled? State any assump- tions clearly.