Question

In a civil lawsuit, the preponderance of evidence for a hypothesis is defined as the amount of evidence needed to make that hypothesis more probable than not. The glove used in committing a murder fits the defendant but only fits 2% of the population. (a) Interpreting the likelihood ratio as the strength of evidence, how strong is the evidence for the hypothesis that the defendant committed the murder? Hint: it would be helpful to use the likelihood function with θ as the parameter, where θ = 1 if the defendant committed the murder and θ = 0 if not.

Answer 1

So, I wrote,

\[\frac{L(1)}{L(0)} = \frac{P(X=x|\theta = 0)}{P(X \neq x|\theta = 1)} = \frac{98}{2}\]

Am I way off?

Answer 2

I got a likelihood of 42, meaning it is significantly favourable evidence that he committed the murder