Nicholas believes that the tomcat Baggins purrs for longer than the female cat Perry, but Caroline, who is a student keenly interested in statistics, asks him to back up his claim by hypothesis testing it with significance \(\alpha=0.1\).

Nicholas then times how long each cat purrs after one single stroke, and gets the following purring durations (in seconds):
- Baggins: 59,71, 102, 64,56, 83 - Perry: \(48,43,51,48,54\).
Assume that the purring durations follow Normal distributions, with respective mean values \(\mu_{B}\) for Baggins and \(\mu_{P}\) for Perry. Use neutral priors and assume \(\sigma\) unknown. Which side has the burden of proof here? To answer this, establish which hypothesis is \(H_{0}\) and which is \(H_{1}\), and decide between the two competing hypotheses.