We now use a maximum likelihood test to compare two random samples from exponential distributions.

Question

Clinical records give the survival time in months from diagnosis of 30 sufferers from a certain disease as

9.73
5.56
4.28
4.87
1.55
6.20
1.08
7.17
28.65
6.10
16.16
9.92
2.40
6.19
7.67
1.11
4.66
4.35
7.31
3.28
13.38
3.08
0.41
4.33
2.16
4.49
0.75
4.45
10.29
0.90

In a clinical trial of a new drug treatment, 21 sufferers had survival times of

22.07
12.47
6.42
8.15
0.64
20.04
17.49
2.22
3.00
28.09
3.94
8.59
4.26
32.82
8.32
2.12
18.53
9.95
4.25
3.70
5.82

Assuming that survival times are exponentially distributed, perform a likelihood ratio test for whether the death rate is different for those getting the new drug.

(Solved in full version)