Assignment:
Question
Consider the data in the following table collected on 15 patients at 5, 10, 15, 20 and 25 days after the treatment.
Time after treatment
Patient 5 10 15 20 25
1 11 18 15 18 15
2 33 27 31 21 17
3 20 28 27 23 29
4 28 26 18 18 18
5 22 23 22 16 10
6 20 22 16 15 12
7 24 27 22 21 24
8 30 26 30 24 20
9 25 30 26 19 25
10 22 25 32 24 30
11 27 27 31 17 20
12 33 28 29 25 31
13 10 15 10 15 15
14 18 21 17 16 22
15 25 18 31 17 19
We may assume that each data point in this table (i.e. each row) comes from a multivariate normal distribution.
(a) Test the hypothesis that the mean responses at different time periods are equal.
(b) It is desirable to determine if the response varies linearly with time. This may be stated as a hypothesis H : t 0 t μ = a + b . Perform a test on H0. (Hint: you may test if the consecutive differences of μ are the same.)
(c) Assume the first 7 individuals in this data set were controls and that the last 8 individuals were treated with the treatment. Test whether these two groups have equal means assuming they have equal covariance matrix.