1. Define the following terms: parameter, pivotal quantity, test statistic, reference distribution, p-value. [5 marks]

2. The table below gives concentration of aspirin in urine (in mg%) for 10 subjects, 1 hour after taking Aspirin A and 1 hour after taking Aspirin B.

Subject:	1	2	3	4	5	6	7	8	9	10
Aspirin A:	14	25	12	27	16	19	6	35	11	17
Aspirin B:	13	10	20	21	17	22	5	30	7	11

(a) Compute a p-value to test the hypothesis that the average difference between the two Aspirins is zero, against a two-sided alternative. [4 marks] State any assumptions you make and do what you can to asses the validity of your assumptions graphically. [4 marks]

(b) Compute a two-sided 95% confidence interval for the standard deviation of the differences. State any assumptions you make. [3 marks]

(c) Compute a p-value to test the hypothesis that the median difference between the two Aspirins is zero, against a two-sided alternative, without assuming normality. [4 marks]

3. You are planning a new, larger, study to compare Aspirin A to Aspirin B. You expect that the true mean difference may be as small as 1 mg% but in all other respects the new study will be like the previous one. You will be testing at the 1% level of significance. What sample size will you need to ensure a type II error rate of 5%? [5 marks]

4. In a genetics experiment, 23 out of 82 drosophila were wild-eyed females. Compute a two-sided 95% confidence interval for the true percentage of wild-eyed females from this cross. Use the confidence interval to test the hypothesis that the true percentage is 25%. State any assumptions you make. [5 marks]