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]